Transmitting apparatus and interleaving method thereof

ABSTRACT

A transmitting apparatus is provided. The transmitting apparatus includes: an encoder configured to generate a low density parity check (LDPC) codeword by LDPC encoding based on a parity check matrix; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the modulator is further configured to map a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.

CROSS-REFERENCE TO THE RELATED APPLICATIONS

This is a continuation of U.S. patent application Ser. No. 15/435,042,filed Feb. 16, 2017, which is a continuation of U.S. patent applicationSer. No. 15/130,204, filed on Apr. 15, 2016, issued as U.S. Pat. No.9,692,454 on Jun. 27, 2017, which is a continuation of U.S. patentapplication Ser. No. 14/625,862, filed Feb. 19, 2015, issued as U.S.Pat. No. 9,602,137 on Mar. 21, 2017, which claims priority from U.S.Provisional Application No. 61/941,676 filed on Feb. 19, 2014, U.S.Provisional Application No. 62/001,170 filed on May 21, 2014, and KoreanPatent Application No. 10-2015-0000671 filed on Jan. 5, 2015. The entiredisclosures of the prior applications are considered part of thedisclosure of this continuation application, and are hereby incorporatedby reference.

BACKGROUND 1. Technical Field

Apparatuses and methods consistent with exemplary embodiments relate toa transmitting apparatus and an interleaving method thereof, and moreparticularly, to a transmitting apparatus which processes data andtransmits the data, and an interleaving method thereof.

2. Description of the Related Art

In the 21st century information-oriented society, broadcastingcommunication services are moving into the era of digitalization,multi-channel, wideband, and high quality. In particular, as highquality digital televisions and portable multimedia player and portablebroadcasting equipments are increasingly used in recent years, there isan increasing demand for methods for supporting various receivingmethods of digital broadcasting services.

In order to meet such demand, standard groups are establishing variousstandards and are providing a variety of services to satisfy users'needs. Therefore, there is a need for a method for providing improvedservices to users with high decoding and receiving performance.

SUMMARY

Exemplary embodiments may overcome the above disadvantages and otherdisadvantages not described above. However, it is understood that theexemplary embodiment are not required to overcome the disadvantagesdescribed above, and may not overcome any of the problems describedabove.

The exemplary embodiments provide a transmitting apparatus which can mapa bit included in a predetermined bit group from among a plurality ofbit groups of a low density parity check (LDPC) codeword onto apredetermined bit of a modulation symbol, and transmit the bit, and aninterleaving method thereof.

According to an aspect of an exemplary embodiment, there is provided atransmitting apparatus which may include: an encoder configured togenerate an LDPC codeword by LDPC encoding based on a parity checkmatrix; an interleaver configured to interleave the LDPC codeword; and amodulator configured to map the interleaved LDPC codeword onto amodulation symbol, wherein the modulator is further configured to map abit included in a predetermined bit group from among a plurality of bitgroups constituting the LDPC codeword onto a predetermined bit of themodulation symbol.

Each of the plurality of bit groups may be formed of M number of bits,and M may be a common divisor of N_(ldpc) and K_(ldpc) and may bedetermined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) is acyclic shift parameter value regarding columns in a column group of aninformation word submatrix of the parity check matrix, N_(ldpc) is alength of the LDPC codeword, and K_(ldpc) is a length of informationword bits of the LDPC codeword.

The interleaver may include: a parity interleaver configured tointerleave parity bits of the LDPC codeword; a group interleaverconfigured to divide the parity-interleaved LDPC codeword by theplurality of bit groups and rearrange an order of the plurality of bitgroups in bit group wise; and a block interleaver configured tointerleave the plurality of bit groups the order of which is rearranged.

The group interleaver may be configured to rearrange the order of theplurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method isQPSK, and the code rate is 13/15, π(j) in Equation 21 may be defined asin Table 36.

The interleaver may include: a group interleaver configured to dividethe LDPC codeword into the plurality of bit groups and rearrange anorder of the plurality of bit groups in bit group wise; and a blockinterleaver configured to interleave the plurality of bit groups theorder of which is rearranged.

The group interleaver may be configured to rearrange the order of theplurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method isQPSK, and the code rate is 5/15, π(j) in Equation 21 is defined as inTable 32.

The block interleaver may be configured to interleave by writing theplurality of bit groups in each of a plurality of columns in bit groupwise in a column direction, and reading each row of the plurality ofcolumns in which the plurality of bit groups are written in bit groupwise in a row direction.

The block interleaver may be configured to serially write, in theplurality of columns, at least some bit groups which are writable in theplurality of columns in bit group wise from among the plurality of bitgroups, and then divide and write the other bit groups in an area whichremains after the at least some bit groups are written in the pluralityof columns in bit group wise.

According to an aspect of another exemplary embodiment, there isprovided an interleaving method of a transmitting apparatus. The methodmay include: generating an LDPC codeword by LDPC encoding based on aparity check matrix; interleaving the LDPC codeword; and mapping theinterleaved LDPC codeword onto a modulation symbol, wherein the mappingincludes mapping a bit included in a predetermined bit group from amonga plurality of bit groups constituting the LDPC codeword onto apredetermined bit of the modulation symbol.

Each of the plurality of bit groups may be formed of M number of bits,and M may be a common divisor of N_(ldpc) and K_(ldpc) and may bedetermined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) is acyclic shift parameter value regarding columns in a column group of aninformation word submatrix of the parity check matrix, N_(ldpc) is alength of the LDPC codeword, and K_(ldpc) is a length of informationword bits of the LDPC codeword.

The interleaving may include: interleaving parity bits of the LDPCcodeword; dividing the parity-interleaved LDPC codeword by the pluralityof bit groups and rearranging an order of the plurality of bit groups inbit group wise; and interleaving the plurality of bit groups the orderof which is rearranged.

The rearranging in bit group wise may include rearranging the order ofthe plurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method isQPSK, and the code rate is 13/15, π(j) in Equation 21 may be defined asin Table 36.

The interleaving may include: dividing the interleaved LDPC codewordinto the plurality of bit groups and rearranging an order of theplurality of bit groups in bit group wise; and interleaving theplurality of bit groups the order of which is rearranged.

The rearranging in bit group wise may include rearranging the order ofthe plurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method isQPSK, and the code rate is 5/15, π(j) in Equation 21 may be defined asin Table 32.

The interleaving the plurality of bit groups may include interleaving bywriting the plurality of bit groups in each of a plurality of columns inbit group wise in a column direction, and reading each row of theplurality of columns in which the plurality of bit groups are written inbit group wise in a row direction.

The interleaving the plurality of bit groups may include seriallywriting, in the plurality of columns, at least some bit groups which arewritable in the plurality of columns in bit group wise from among theplurality of bit groups, and then dividing and writing the other bitgroups in an area which remains after the at least some bit groups arewritten in the plurality of columns in bit group wise.

According to various exemplary embodiments, improved decoding andreceiving performance can be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describing indetail exemplary embodiments, with reference to the accompanyingdrawings, in which:

FIG. 1 is a block diagram to illustrate a configuration of atransmitting apparatus according to an exemplary embodiment;

FIGS. 2 to 4 illustrate a configuration of a parity check matrixaccording to various exemplary embodiments;

FIG. 5 is a block diagram to illustrate a configuration of aninterleaver according to an exemplary embodiment;

FIGS. 6 to 8 illustrate an interleaving method according to exemplaryembodiments;

FIGS. 9 to 15 illustrate an interleaving method of a block interleaveraccording to exemplary embodiments;

FIG. 16 illustrates an operation of a demultiplexer according to anexemplary embodiment;

FIGS. 17 to 19 illustrate a method for extracting interleavingparameters according to exemplary embodiments;

FIG. 20 is a block diagram to illustrate a configuration of a receivingapparatus according to an exemplary embodiment;

FIG. 21 is a block diagram to illustrate a configuration of adeinterleaver according to an exemplary embodiment;

FIG. 22 illustrates a deinterleaving method of a block deinterleaveraccording to an exemplary embodiment; and

FIG. 23 is a flowchart to illustrate an interleaving method according toan exemplary embodiment.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Hereinafter, various exemplary embodiments will be described in greaterdetail with reference to the accompanying drawings.

In the following description, same reference numerals are used for thesame elements when they are depicted in different drawings. The mattersdefined in the description, such as detailed construction and elements,are provided to assist in a comprehensive understanding of the exemplaryembodiments. Thus, it is apparent that the exemplary embodiments can becarried out without those specifically defined matters. Also, functionsor elements known in the related art are not described in detail sincethey would obscure the exemplary embodiments with unnecessary detail.

FIG. 1 is a block diagram to illustrate a configuration of atransmitting apparatus according to an exemplary embodiment. Referringto FIG. 1, the transmitting apparatus 100 includes an encoder 110, aninterleaver 120, and a modulator 130 (or a constellation mapper).

The encoder 110 generates a low density parity check (LDPC) codeword byperforming LDPC encoding based on a parity check matrix. To achievethis, the encoder 110 may include an LDPC encoder (not shown) to performthe LDPC encoding.

Specifically, the encoder 110 LDPC-encodes information word (orinformation) bits to generate the LDPC codeword which is formed of theinformation word bits and parity bits (that is, LDPC parity bits). Here,bits input to the encoder 110 may be used to the information word bits.Also, since an LDPC code is a systematic code, the information word bitsmay be included in the LDPC codeword as they are.

The LDPC codeword is formed of the information word bits and the paritybits. For example, the LDPC codeword is formed of N_(ldpc) number ofbits, and includes K_(ldpc) number of information word bits andN_(parity)=N_(ldpc)−K_(ldpc) number of parity bits.

In this case, the encoder 110 may generate the LDPC codeword byperforming the LDPC encoding based on the parity check matrix. That is,since the LDPC encoding is a process for generating an LDPC codeword tosatisfy H·C^(T)=0, the encoder 110 may use the parity check matrix whenperforming the LDPC encoding. Herein, H is a parity check matrix and Cis an LDPC codeword.

For the LDPC encoding, the transmitting apparatus 100 may include amemory and may pre-store parity check matrices of various formats.

For example, the transmitting apparatus 100 may pre-store parity checkmatrices which are defined in Digital Video Broadcasting-Cable version 2(DVB-C2), Digital Video Broadcasting-Satellite-Second Generation(DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial(DVB-T2), etc., or may pre-store parity check matrices which are definedin the North America digital broadcasting standard system AdvancedTelevision System Committee (ATSC) 3.0 standards, which are currentlybeing established. However, this is merely an example and thetransmitting apparatus 100 may pre-store parity check matrices of otherformats in addition to these parity check matrices.

Hereinafter, a parity check matrix according to various exemplaryembodiments will be explained in detail with reference to the drawings.In the parity check matrix, elements other than elements having 1 have0.

For example, the parity check matrix according to an exemplaryembodiment may have a configuration of FIG. 2.

Referring to FIG. 2, a parity check matrix 200 is formed of aninformation word submatrix (or an information submatrix) 210corresponding to information word bits, and a parity submatrix 220corresponding to parity bits.

The information word submatrix 210 includes K_(ldpc) number of columnsand the parity submatrix 220 includes N_(parity)=N_(ldpc)−K_(ldpc)number of columns. The number of rows of the parity check matrix 200 isidentical to the number of columns of the parity submatrix 220,N_(panty)=N_(ldpc)−K_(ldpc).

In addition, in the parity check matrix 200, N_(ldpc) is a length of anLDPC codeword, K_(ldpc) is a length of information word bits, andN_(parity)=N_(ldpc)−K_(ldpc) is a length of parity bits. The length ofthe LDPC codeword, the information word bits, and the parity bits meanthe number of bits included in each of the LDPC codeword, theinformation word bits, and the parity bits.

Hereinafter, the configuration of the information word submatrix 210 andthe parity submatrix 220 will be explained in detail.

The information word submatrix 210 includes K_(ldpc) number of columns(that is, 0^(th) column to (K_(ldpc)−1)^(th) column), and follows thefollowing rules:

First, M number of columns from among K_(ldpc) number of columns of theinformation word submatrix 210 belong to the same group, and K_(ldpc)number of columns is divided into K_(ldpc)/M number of column groups. Ineach column group, a column is cyclic-shifted from an immediatelyprevious column by Q_(ldpc). That is, Q_(ldpc) may be a cyclic shiftparameter value regarding columns in a column group of the informationword submatrix 210 of the parity check matrix 200.

Herein, M is an interval at which a pattern of a column group, whichincludes a plurality of columns, is repeated in the information wordsubmatrix 210 (e.g., M=360), and Q_(ldpc) is a size by which one columnis cyclic-shifted from an immediately previous column in a same columngroup in the information word submatrix 210. Also, M is a common divisorof N_(ldpc) and K_(ldpc) and is determined to satisfyQ_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Here, M and Q_(ldpc) are integers andK_(ldpc)/M is also an integer. M and Q_(ldpc) may have various valuesaccording to a length of the LDPC codeword and a code rate (CR)(or,coding rate).

For example, when M=360 and the length of the LDPC codeword, N_(ldpc),is 64800, Q_(ldpc) may be defined as in Table 1 presented below, and,when M=360 and the length N_(ldpc) of the LDPC codeword is 16200,Q_(ldpc) may be defined as in Table 2 presented below.

TABLE 1 Code Rate N_(ldpc) M Q_(ldpc)  5/15 64800 360 120  6/15 64800360 108  7/15 64800 360 96  8/15 64800 360 84  9/15 64800 360 72 10/1564800 360 60 11/15 64800 360 48 12/15 64800 360 36 13/15 64800 360 24

TABLE 2 Code Rate N_(ldpc) M Q_(ldpc)  5/15 16200 360 30  6/15 16200 36027  7/15 16200 360 24  8/15 16200 360 21  9/15 16200 360 18 10/15 16200360 15 11/15 16200 360 12 12/15 16200 360 9 13/15 16200 360 6

Second, when the degree of the 0^(th) column of the i^(th) column group(i=0, 1, . . . , K_(ldpc)/M−1) is D_(i) (herein, the degree is thenumber of value 1 existing in each column and all columns belonging tothe same column group have the same degree), and a position (or anindex) of each row where 1 exists in the 0^(th) column of the i^(th)column group is R_(i,0) ⁽⁰⁾R_(i,0) ⁽¹⁾, . . . , R_(i,0) ^((D) ^(i) ⁻¹⁾,an index R_(i,j) ^((k)) of a row where k^(th) 1 is located in the j^(th)column in the i^(th) column group is determined by following Equation 1:

R _(i,j) ^((k)) =R _(i,(j-1)) ^((k)) +Q _(ldpc) mod(N _(ldpc) −K_(ldpc))  (1),

where k=0, 1, 2, . . . D₁−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1, 2, .. . , M−1.

Equation 1 can be expressed as following Equation 2:

R _(i,j) ^((k)) ={R _(i,0) ^((k))+(j mod M)×Q _(ldpc)} mod(N _(ldpc) −K_(ldpc))  (2),

where k=0, 1, 2, . . . D₁−1; i=0, 1, K_(ldpc)/M−1; and j=1, 2, . . . ,M−1. Since j=1, 2, . . . , M−1, (j mod M) of Equation 2 may be regardedas j.

In the above equations, R_(i,j) ^((k)) is an index of a row where k^(th)1 is located in the j^(th) column in the i^(th) column group, N_(ldpc)is a length of an LDPC codeword, K_(ldpc) is a length of informationword bits, D_(i) is a degree of columns belonging to the i^(th) columngroup, M is the number of columns belonging to a single column group,and Q_(ldpc) is a size by which each column in the column group iscyclic-shifted.

As a result, referring to these equations, when only R_(i,0) ^((k)) isknown, the index R_(i,j) ^((k)) of the row where the k^(th) 1 is locatedin the j^(th) column in the i^(th) column group can be known. Therefore,when the index value of the row where the k^(th) 1 is located in the0^(th) column of each column group is stored, a position of column androw where 1 is located in the parity check matrix 200 having theconfiguration of FIG. 2 (that is, in the information word submatrix 210of the parity check matrix 200) can be known.

According to the above-described rules, all of the columns belonging tothe i^(th) column group have the same degree D_(i). Accordingly, theLDPC codeword which stores information on the parity check matrixaccording to the above-described rules may be briefly expressed asfollows.

For example, when N_(ldpc) is 30, K_(ldpc) is 15, and Q_(ldpc) is 3,position information of the row where 1 is located in the 0^(th) columnof the three column groups may be expressed by a sequence of Equations 3and may be referred to as “weight-1 position sequence”.

R _(1,0) ⁽¹⁾=1,R _(1,0) ⁽²⁾=2,R _(1,0) ⁽³⁾=8,R _(1,0) ⁽⁴⁾=10,

R _(2,0) ⁽¹⁾=0,R _(2,0) ⁽²⁾=9,R _(2,0) ⁽³⁾=13,

R _(3,0) ⁽¹⁾=0,R _(3,0) ⁽²⁾=14.  (3),

where R_(i,j) ^((k)) is an index of a row where k^(th) 1 is located inthe j^(th) column in the i^(th) column group.

The weight-1 position sequence like Equation 3 which expresses an indexof a row where 1 is located in the 0^(th) column of each column groupmay be briefly expressed as in Table 3 presented below:

TABLE 3   1 2 8 10 0 9 13 0 14

Table 3 shows positions of elements having value 1 in the parity checkmatrix, and the i^(th) weight-1 position sequence is expressed byindexes of rows where 1 is located in the 0^(th) column belonging to thei^(th) column group.

The information word submatrix 210 of the parity check matrix accordingto an exemplary embodiment may be defined as in Tables 4 to 21 presentedbelow, based on the above descriptions.

Specifically, Tables 4 to 21 show indexes of rows where 1 is located inthe 0^(th) column of the i^(th) column group of the information wordsubmatrix 210. That is, the information word submatrix 210 is formed ofa plurality of column groups each including M number of columns, andpositions of 1 in the 0^(th) column of each of the plurality of columngroups may be defined by Tables 4 to 21.

Herein, the indexes of the rows where 1 is located in the 0^(th) columnof the i^(th) column group mean “addresses of parity bit accumulators”.The “addresses of parity bit accumulators” have the same meaning asdefined in the DVB-C2/S2/T2 standards or the ATSC 3.0 standards whichare currently being established, and thus, a detailed explanationthereof is omitted.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, thecode rate is 5/15, and M is 360, the indexes of the rows where 1 islocated in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are as shown in Table 4 presented below:

TABLE 4 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 245 449 491 980 1064 1194 1277 1671 2026 3186 4399 49005283 5413 5558 6570 7492 7768 7837 7984 8306 8483 8685 9357 9642 1004510179 10261 10338 10412 1 1318 1584 1682 1860 1954 2000 2062 3387 34413879 3931 4240 4302 4446 4603 5117 5588 5675 5793 5955 6097 6221 64496616 7218 7394 9535 9896 10009 10763 2 105 472 785 911 1168 1450 25502851 3277 3624 4128 4460 4572 4669 4783 5102 5133 5199 5905 6647 70287086 7703 8121 8217 9149 9304 9476 9736 9884 3 1217 5338 5737 8334 4 855994 2979 9443 5 7506 7811 9212 9982 6 848 3313 3380 3990 7 2095 41134620 9946 8 1488 2396 6130 7483 9 1002 2241 7067 10418 10 2008 3199 72157502 11 1161 7705 8194 8534 12 2316 4803 8649 9359 13 125 1880 3177 141141 8033 9072

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 5 or 6presented below:

TABLE 5 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 432 655 893 942 1285 1427 1738 2199 2441 2565 2932 32014144 4419 4678 4963 5423 5922 6433 6564 6656 7478 7514 7892 1 220 453590 826 1116 1425 1488 1901 3119 3182 3568 3800 3953 4071 4782 5038 55556836 6871 7131 7609 7850 8317 8443 2 300 454 497 930 1757 2145 2314 23722467 2819 3191 3256 3699 3984 4538 4965 5461 5742 5912 6135 6649 76368078 8455 3 24 65 565 609 990 1319 1394 1465 1918 1976 2463 2987 33303677 4195 4240 4947 5372 6453 6950 7066 8412 8500 8599 4 1373 4663 53247777 5 189 3930 5766 6877 6 3 2961 4207 5747 7 1108 4768 6743 7106 81282 2274 2750 6204 9 2279 2587 2737 6344 10 2889 3164 7275 8040 11 1332734 5081 8386 12 437 3203 7121 13 4280 7128 8490 14 619 4563 6206 152799 6814 6991 16 244 4212 5925 17 1719 7657 8554 18 53 1895 6685 19 5845420 6856 20 2958 5834 8103

TABLE 6 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 553 742 9011327 1544 2179 2519 3131 3280 3603 378937924253 5340 5934 5962 6004 6698 7793 8001 8058 8126 8276 8559 1 503590 598 1185 1266 1336 1806 2473 3021 3356 3490 3680 3936 4501 4659 58916132 6340 6602 7447 8007 8045 80598249 2 795 831 9471330 1502 2041 23282513 2814 2829 4048 4802 6044 6109 6461 6777 6800 7099 7126 8095 84288519 8556 8610 3 601 787 8991757 2259 2518 2783 2816 2823 2949 339643304494 4684 4700 4837 4881 4975 5130 5464 65546912 7094 8297 4 42295628 7917 7992 5 1506 3374 4174 5547 6 4275 5650 8208 8533 7 1504 17473433 6345 8 3659 6955 7575 7852 9 607 3002 4913 6453 10 3533 6850 78958048 11 4094 6366 8314 12 2206 4513 5411 13 32 3882 5149 14 389 31214626 15 1308 4419 6520 16 2092 2373 6849 17 1815 3679 7152 18 3582 39796948 19 1049 2135 3754 20 2276 4442 6591

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 7 or 8presented below:

TABLE 7 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 350 462 1291 1383 1821 2235 2493 3328 3353 3772 3872 39234259 4426 4542 4972 5347 6217 6246 6332 6386 1 177 859 1214 1253 13981482 1737 2014 2161 2331 3108 3297 3438 4388 4430 4456 4522 4783 52736037 6395 2 347 501 658 966 1622 1659 1934 2117 2527 3168 3231 3379 34273739 4218 4497 4894 5000 5167 5728 5975 3 319 398 599 1143 1796 31983521 3886 4139 4453 4556 4636 4688 4753 4986 5199 5224 5496 5698 57246123 4 162 257 304 524 945 1695 1855 2527 2780 2902 2958 3439 3484 42244769 4928 5156 5303 5971 6358 6477 5 807 1695 2941 4276 6 2652 2857 46606358 7 329 2100 2412 3632 8 1151 1231 3872 4869 9 1561 3565 5138 5303 10407 794 1455 11 3438 5683 5749 12 1504 1985 3563 13 440 5021 6321 14 1943645 5923 15 1217 1462 6422 16 1212 4715 5973 17 4098 5100 5642 18 55125857 6226 19 2583 5506 5933 20 784 1801 4890 21 4734 4779 4875 22 9385081 5377 23 127 4125 4704 24 1244 2178 3352 25 3659 6350 6465 26 16863464 4336

TABLE 8 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 212 255 540 967 1033 1517 1538 3124 3408 3800 4373 48644905 5163 5177 6186 1 275 660 1351 2211 28763063 3433 4088 4273 45444618 4632 5548 6101 6111 6136 2 279 335 494865 1662 1681 3414 3775 425245955272 5471 5796 5907 5986 6008 3 345 352 3094 3188 42974338 4490 48655303 6477 4 222 681 1218 3169 3850 4878 4954 5666 6001 6237 5 172 5121536 1559 21792227 3334 4049 6464 6 716 934 1694 2890 3276 3608 43324468 5945 7 1133 1593 1825 2571 3017 4251 5221 5639 5845 8 1076 12226465 9 159 5064 6078 10 374 4073 5357 11 2833 5526 5845 12 1594 36395419 13 1028 1392 4239 14 115 622 2175 15 300 1748 6245 16 2724 32765349 17 1433 6117 6448 18 485 663 4955 19 711 1132 4315 20 177 3266 433921 1171 4841 4982 22 33 1584 3692 23 2820 3485 4249 24 1716 2428 3125 25250 2275 6338 26 108 1719 4961

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 11/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 9 or 10presented below:

TABLE 9 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 108 297 703 742 1345 1443 1495 1628 1812 2341 2559 26692810 2877 3442 3690 3755 3904 4264 1 180 211 477 788 824 1090 1272 15781685 1948 2050 2195 2233 2546 2757 2946 3147 3299 3544 2 627 741 11351157 1226 1333 1378 1427 1454 1696 1757 1772 2099 2208 2592 3354 35804066 4242 3 9 795 959 989 1006 1032 1135 1209 1382 1484 1703 1855 19852043 2629 2845 3136 3450 3742 4 230 413 801 829 1108 1170 1291 1759 17931827 1976 2000 2423 2466 2917 3010 3600 3782 4143 5 56 142 236 381 10501141 1372 1627 1985 2247 2340 3023 3434 3519 3957 4013 4142 4164 4279 6298 1211 2548 3643 7 73 1070 1614 1748 8 1439 2141 3614 9 284 1564 262910 607 660 855 11 1195 2037 2753 12 49 1198 2562 13 296 1145 3540 141516 2315 2382 15 154 722 4016 16 759 2375 3825 17 162 194 1749 18 23352422 2632 19 6 1172 2583 20 726 1325 1428 21 985 2708 2769 22 255 28013181 23 2979 3720 4090 24 208 1428 4094 25 199 3743 3757 26 1229 20594282 27 458 1100 1387 28 1199 2481 3284 29 1161 1467 4060 30 959 30144144 31 2665 3960 4125 32 2809 3834 4318

TABLE 10 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 49 719 784 794 968 2382 2685 2873 2974 2995 3540 4179 1272 281 374 1279 2034 2067 2112 3429 3613 3815 3838 4216 2 206 714 8201800 1925 2147 2168 2769 2806 3253 3415 4311 3 62 159 166 605 1496 17112652 3016 3347 3517 3654 4113 4 363 733 1118 2062 2613 2736 3143 34273664 4100 4157 4314 5 57 142 436 983 1364 2105 2113 3074 3639 3835 41644242 6 870 921 950 1212 1861 2128 2707 2993 3730 3968 3983 4227 7 1852684 3263 8 2035 2123 2913 9 883 2221 3521 10 1344 1773 4132 11 438 31783650 12 543 756 1639 13 1057 2337 2898 14 171 3298 3929 15 1626 29603503 16 484 3050 3323 17 2283 2336 4189 18 2732 4132 4318 19 225 23353497 20 600 2246 2658 21 1240 2790 3020 22 301 1097 3539 23 1222 12672594 24 1364 2004 3603 25 1142 1185 2147 26 564 1505 2086 27 697 9912908 28 1467 2073 3462 29 2574 2818 3637 30 748 2577 2772 31 1151 14194129 32 164 1238 3401

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 13/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 11 or 12presented below:

TABLE 11 Index of row where 1 is located in the 0th column of the ith icolumn group 0 37 144 161 199 220 496 510 589 731 808 834 965 1249 12641311 1377 1460 1520 1598 1707 1958 2055 2099 2154 1 20 27 165 462 546583 742 796 1095 1110 1129 1145 1169 1190 1254 1363 1383 1463 1718 18351870 1879 2108 2128 2 288 362 463 505 638 691 745 861 1006 1083 11241175 1247 1275 1337 1353 1378 1506 1588 1632 1720 1868 1980 2135 3 405464 478 511 566 574 641 766 785 802 836 996 1128 1239 1247 1449 14911537 1616 1643 1668 1950 1975 2149 4 86 192 245 357 363 374 700 713 852903 992 1174 1245 1277 1342 1369 1381 1417 1463 1712 1900 1962 2053 21185 101 327 378 550 6 186 723 1318 1550 7 118 277 504 1835 8 199 407 17761965 9 387 1253 1328 1975 10 62 144 1163 2017 11 100 475 572 2136 12 431865 1568 2055 13 283 640 981 1172 14 220 1038 1903 2147 15 483 1318 13582118 16 92 961 1709 1810 17 112 403 1485 2042 18 431 1110 1130 1365 19587 1005 1206 1588 20 704 1113 1943 21 375 1487 2100 22 1507 1950 211023 962 1613 2038 24 554 1295 1501 25 488 784 1446 26 871 1935 1964 27 541475 1504 28 1579 1617 2074 29 1856 1967 2131 30 330 1582 2107 31 401056 1809 32 1310 1353 1410 33 232 554 1939 34 168 641 1099 35 333 4371556 36 153 622 745 37 719 931 1188 38 237 638 1607

TABLE 12 Index of row where 1 is located in the 0th column of the ith icolumn group 0 71 334 645 779 786 1124 1131 1267 1379 1554 1766 17981939 1 6 183 364 506 512 922 972 981 1039 1121 1537 1840 2111 2 6 71 153204 253 268 781 799 873 1118 1194 1661 2036 3 6 247 353 581 921 940 11081146 1208 1268 1511 1527 1671 4 6 37 466 548 747 1142 1203 1271 15121516 1837 1904 2125 5 6 171 863 953 1025 1244 1378 1396 1723 1783 18161914 2121 6 1268 1360 1647 1769 7 6 458 1231 1414 8 183 535 1244 1277 9107 360 498 1456 10 6 2007 2059 2120 11 1480 1523 1670 1927 12 139 573711 1790 13 6 1541 1889 2023 14 6 374 957 1174 15 287 423 872 1285 16 61809 1918 17 65 818 1396 18 590 766 2107 19 192 814 1843 20 775 11631256 21 42 735 1415 22 334 1008 2055 23 109 596 1785 24 406 534 1852 25684 719 1543 26 401 465 1040 27 112 392 621 28 82 897 1950 29 887 19622125 30 793 1088 2159 31 723 919 1139 32 610 839 1302 33 218 1080 181634 627 1646 1749 35 496 1165 1741 36 916 1055 1662 37 182 722 945 38 5595 1674

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 13 presentedbelow:

TABLE 13 Index of row where 1 is located in the 0th column of the ith icolumn group 0 1606 3402 4961 6751 7132 11516 12300 12482 12592 1334213764 14123 21576 23946 24533 25376 25667 26836 31799 34173 35462 3615336740 37085 37152 37468 37658 1 4621 5007 6910 8732 9757 11508 1309915513 16335 18052 19512 21319 23663 25628 27208 31333 32219 33003 3323933447 36200 36473 36938 37201 37283 37495 38642 2 16 1094 2020 3080 41945098 5631 6877 7889 8237 9804 10067 11017 11366 13136 13354 15379 1893420199 24522 26172 28666 30386 32714 36390 37015 37162 3 700 897 17086017 6490 7372 7825 9546 10398 16605 18561 18745 21625 22137 23693 2434024966 25015 26995 28586 28895 29687 33938 34520 34858 37056 38297 4 1592010 2573 3617 4452 4958 5556 5832 6481 8227 9924 10836 14954 1559416623 18065 19249 22394 22677 23408 23731 24076 24776 27007 28222 3034338371 5 3118 3545 4768 4992 5227 6732 8170 9397 10522 11508 15536 2021821921 28599 29445 29758 29968 31014 32027 33685 34378 35867 36323 3672836870 38335 38623 6 1264 4254 6936 9165 9486 9950 10861 11653 1369713961 15164 15665 18444 19470 20313 21189 24371 26431 26999 28086 2825129261 31981 34015 35850 36129 37186 7 111 1307 1628 2041 2524 5358 79888191 10322 11905 12919 14127 15515 15711 17061 19024 21195 22902 2372724401 24608 25111 25228 27338 35398 37794 38196 8 961 3035 7174 794813355 13607 14971 18189 18339 18665 18875 19142 20615 21136 21309 2175823366 24745 25849 25982 27583 30006 31118 32106 36469 36583 37920 9 29903549 4273 4808 5707 6021 6509 7456 8240 10044 12262 12660 13085 1475015680 16049 21587 23997 25803 28343 28693 34393 34860 35490 36021 3773738296 10 955 4323 5145 6885 8123 9730 11840 12216 19194 20313 2305624248 24830 25268 26617 26801 28557 29753 30745 31450 31973 32839 3302533296 35710 37366 37509 11 264 605 4181 4483 5156 7238 8863 10939 1125112964 16254 17511 20017 22395 22818 23261 23422 24064 26329 27723 2818630434 31956 33971 34372 36764 38123 12 520 2562 2794 3528 3860 4402 56766963 8655 9018 9783 11933 16336 17193 17320 19035 20606 23579 2376924123 24966 27866 32457 34011 34499 36620 37526 13 10106 10637 1090634242 14 1856 15100 19378 21848 15 943 11191 27806 29411 16 4575 635913629 19383 17 4476 4953 18782 24313 18 5441 6381 21840 35943 19 96389763 12546 30120 20 9587 10626 11047 25700 21 4088 15298 28768 35047 222332 6363 8782 28863 23 4625 4933 28298 30289 24 3541 4918 18257 3174625 1221 25233 26757 34892 26 8150 16677 27934 30021 27 8500 25016 3304338070 28 7374 10207 16189 35811 29 611 18480 20064 38261 30 25416 2735236089 38469 31 1667 17614 25839 32776 32 4118 12481 21912 37945 33 557313222 23619 31271 34 18271 26251 27182 30587 35 14690 26430 26799 3435536 13688 16040 20716 34558 37 2740 14957 23436 32540 38 3491 14365 1468136858 39 4796 6238 25203 27854 40 1731 12816 17344 26025 41 19182 2166223742 27872 42 6502 13641 17509 34713 43 12246 12372 16746 27452 44 158921528 30621 34003 45 12328 20515 30651 31432 46 3415 22656 23427 3639547 632 5209 25958 31085 48 619 3690 19648 37778 49 9528 13581 2696536447 50 2147 26249 26968 28776 51 15698 18209 30683 52 1132 19888 3411153 4608 25513 38874 54 475 1729 34100 55 7348 32277 38587 56 182 1647333082 57 3865 9678 21265 58 4447 20151 27618 59 6335 14371 38711 60 7049695 28858 61 4856 9757 30546 62 1993 19361 30732 63 756 28000 29138 643821 24076 31813 65 4611 12326 32291 66 7628 21515 34995 67 1246 1329430068 68 6466 33233 35865 69 14484 23274 38150 70 21269 36411 37450 7123129 26195 37653

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 7/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 14 presentedbelow:

TABLE 14 Index of row where 1 is located in the 0th column of the ith icolumn group 0 7 15 26 69 1439 3712 5756 5792 5911 8456 10579 1946219782 21709 23214 25142 26040 30206 30475 31211 31427 32105 32989 3308233502 34116 34241 34288 34292 34318 34373 34390 34465 1 83 1159 22716500 6807 7823 10344 10700 13367 14162 14242 14352 15015 17301 1895220811 24974 25795 27868 28081 33077 33204 33262 33350 33516 33677 3368033930 34090 34250 34290 34377 34398 2 25 2281 2995 3321 6006 7482 842811489 11601 14011 17409 26210 29945 30675 31101 31355 31421 31543 3169732056 32216 33282 33453 33487 33696 34044 34107 34213 34247 34261 3427634467 34495 3 0 43 87 2530 4485 4595 9951 11212 12270 12344 15566 2133524699 26580 28518 28564 28812 29821 30418 31467 31871 32513 32597 3318733402 33706 33838 33932 33977 34084 34283 34440 34473 4 81 3344 55407711 13308 15400 15885 18265 18632 22209 23657 27736 29158 29701 2984530409 30654 30855 31420 31604 32519 32901 33267 33444 33525 33712 3387834031 34172 34432 34496 34502 34541 5 42 50 66 2501 4706 6715 6970 86379999 14555 22776 26479 27442 27984 28534 29587 31309 31783 31907 3192731934 32313 32369 32830 33364 33434 33553 33654 33725 33889 33962 3446734482 6 6534 7122 8723 13137 13183 15818 18307 19324 20017 26389 2932631464 32678 33668 34217 7 50 113 2119 5038 5581 6397 6550 10987 2230825141 25943 29299 30186 33240 33399 8 7262 8787 9246 10032 10505 1309014587 14790 16374 19946 21129 25726 31033 33660 33675 9 5004 5087 52917949 9477 11845 12698 14585 15239 17486 18100 18259 21409 21789 24280 1028 82 3939 5007 6682 10312 12485 14384 21570 25512 26612 26854 3037131114 32689 11 437 3055 9100 9517 12369 19030 19950 21328 24196 2423625928 28458 30013 32181 33560 12 18 3590 4832 7053 8919 21149 2425626543 27266 30747 31839 32671 33089 33571 34296 13 2678 4569 4667 65517639 10057 24276 24563 25818 26592 27879 28028 29444 29873 34017 14 7277 2874 9092 10041 13669 20676 20778 25566 28470 28888 30338 31772 3214333939 15 296 2196 7309 11901 14025 15733 16768 23587 25489 30936 3153333749 34331 34431 34507 16 6 8144 12490 13275 14140 18706 20251 2064421441 21938 23703 34190 34444 34463 34495 17 5108 14499 15734 1922224695 25667 28359 28432 30411 30720 34161 34386 34465 34511 34522 18 6189 3042 5524 12128 22505 22700 22919 24454 30526 33437 34114 34188 3449034502 19 11 83 4668 4856 6361 11633 15342 16393 16958 26613 29136 3091732559 34346 34504 20 3185 9728 25062 21 1643 5531 21573 22 2285 608824083 23 78 14678 19119 24 49 13705 33535 25 21192 32280 32781 26 1075321469 22084 27 10082 11950 13889 28 7861 25107 29167 29 14051 3417134430 30 706 894 8316 31 29693 30445 32281 32 10202 30964 34448 33 1581532453 34463 34 4102 21608 24740 35 4472 29399 31435 36 1162 7118 2322637 4791 33548 34096 38 1084 34099 34418 39 1765 20745 33714 40 130221300 33655 41 33 8736 16646 42 53 18671 19089 43 21 572 2028 44 333911506 16745 45 285 6111 12643 46 27 10336 11586 47 21046 32728 34538 4822215 24195 34026 49 19975 26938 29374 80 16473 26777 34212 51 20 2926032784 52 35 31645 32837 53 26132 34410 34495 54 12446 20649 26851 556796 10992 31061 56 0 46 8420 57 10 636 22885 58 7183 16342 18305 59 15604 28258 60 6071 18675 34489 61 16786 25023 33323 62 3573 5081 1092563 5067 31761 34415 64 3735 33534 34522 65 85 32829 34518 66 6555 2336834559 67 22083 29335 29390 68 6738 21110 34316 69 120 4192 11123 70 33134144 20824 71 27783 28550 31034 72 6597 8164 34427 73 18009 23474 3246074 94 6342 12656 75 17 31962 34535 76 15091 24955 28545 77 15 3213 2829878 26562 30236 34537 79 16832 20334 24628 80 4841 20669 26509 81 1805523700 34534 82 23576 31496 34492 83 10699 13826 34440

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 8/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 15 presentedbelow:

TABLE 15 Index of row where 1 is located in the 0th column of the ith icolumn group 0 2768 3039 4059 5856 6245 7013 8157 9341 9802 10470 1152112083 16610 18361 20321 24601 27420 28206 29788 1 2739 8244 8891 915712624 12973 15534 16622 16919 18402 18780 19854 20220 20543 22306 2554027478 27678 28053 2 1727 2268 6246 7815 9010 9556 10134 10472 1138914599 15719 16204 17342 17666 18850 22058 25579 25860 29207 3 28 13463721 5565 7019 9240 12355 13109 14800 16040 16839 17369 17631 1935719473 19891 20381 23911 29683 4 869 2450 4386 5316 6160 7107 10362 1113211271 13149 16397 16532 17113 19894 22043 22784 27383 28615 28804 5 5084292 5831 8559 10044 10412 11283 14810 15888 17243 17538 19903 2052822090 22652 27235 27384 28208 28485 6 389 2248 5840 6043 7000 9054 1107511760 12217 12565 13587 15403 19422 19528 21493 25142 27777 28566 287027 1015 2002 5764 6777 9346 9629 11039 11153 12690 13068 13990 1684117702 20021 24106 26300 29332 30081 30196 8 1480 3084 3467 4401 47985187 7851 11368 12323 14325 14546 16360 17158 18010 21333 25612 2655626906 27005 9 6925 8876 12392 14529 15253 15437 19226 19950 20321 2302123651 24393 24653 26668 27205 28269 28529 29041 29292 10 2547 3404 35384666 5126 5468 7695 8799 14732 15072 15881 17410 18971 19609 19717 2215024941 27908 29018 11 888 1581 2311 5511 7218 9107 10454 12252 1366215714 15894 17025 18671 24304 25316 25556 28489 28977 29212 12 1047 14941718 4645 5030 6811 7868 8146 10611 15767 17682 18391 22614 23021 2376325478 26491 29088 29757 13 59 1781 1900 3814 4121 8044 8906 9175 1115614841 15789 16033 16755 17292 18550 19310 22505 29567 29850 14 1952 30574399 9476 10171 10769 11335 11569 15002 19501 20621 22642 23452 2436025109 25290 25828 28503 29122 15 2895 3070 3437 4764 4905 6670 924411845 13352 13573 13975 14600 15871 17996 19672 20079 20579 25327 2795816 612 1528 2004 4244 4599 4926 5843 7684 10122 10443 12267 14368 1841319058 22985 24257 26202 26596 27899 17 1361 2195 4146 6708 7158 75389138 9998 14862 15359 16076 18925 21401 21573 22503 24146 24247 2777829312 18 5229 6235 7134 7655 9139 13527 15408 16058 16705 18320 1990920901 22238 22437 23654 25131 27550 28247 29903 19 697 2035 4887 52756909 9166 11805 15338 16381 18403 20425 20688 21547 24590 25171 2672628848 29224 29412 20 5379 17329 22659 23062 21 11814 14759 22329 2293622 2423 2811 10296 12727 23 8460 15260 16769 17290 24 14191 14608 2953630187 25 7103 10069 20111 22850 26 4285 15413 26448 29069 27 548 21379189 10928 28 4581 707 23382 23949 29 3942 17248 19486 27922 30 866810230 16922 26678 31 6158 9980 13788 28198 32 12422 16076 24206 29887 338778 10649 18747 22111 34 21029 22677 27150 28980 35 7918 15423 2767227803 36 5927 18086 23525 37 3397 15058 30224 38 24016 25880 26268 391096 4775 7912 40 3259 17301 20802 41 129 8396 15132 42 17825 2811928676 43 2343 8382 28840 44 3907 18374 20939 45 1132 1290 8786 46 14814710 28846 47 2185 3705 26834 48 5496 15681 21854 49 12697 13407 2217850 12788 21227 22894 51 629 2854 6232 52 2289 18227 27458 53 7593 2193523001 54 3836 7081 12282 55 7925 18440 23135 56 497 6342 9717 57 1119922046 30067 58 12572 28045 28990 59 1240 2023 10933 60 19566 20629 2518661 6442 13303 28813 62 4765 10572 16180 63 552 19301 24286 64 6782 1848021383 65 11267 12288 15758 66 771 5652 15531 67 16131 20047 25649 6813227 23035 24450 69 4839 13467 27488 70 2852 4677 22993 71 2504 2811629524 72 12518 17374 24267 73 1222 11859 27922 74 9660 17286 18261 75232 11296 29978 76 9750 11165 16295 77 4894 9505 23622 78 10861 1198014110 79 2128 15883 22836 80 6274 17243 21989 81 10866 13202 22517 8211159 16111 21608 83 3719 18787 22100 84 1756 2020 23901 85 20913 2947330103 86 2729 15091 26976 87 4410 8217 12963 88 5395 24564 28235 89 385917909 23051 90 5733 26005 29797 91 1935 3492 29773 92 11903 21380 2991493 6091 10469 29997 94 2895 8930 15594 95 1827 10028 20070

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 9/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 16 presentedbelow:

TABLE 16 Index of row where 1 is located in the 0th column of the ith icolumn group 0 113 1557 3316 5680 6241 10407 13404 13947 14040 1435315522 15698 16079 17363 19374 19543 20530 22833 24339 1 271 1361 62367006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 2393825351 25590 25876 25910 2 73 605 872 4008 6279 7653 10346 10799 1248212935 13604 15909 16526 19782 20506 22804 23629 24859 25600 3 1445 16904304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 2195822451 23869 23999 24177 4 1290 2337 5661 6371 8996 10102 10941 1136012242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913 5 2842 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 2333623367 23890 24061 25657 25680 6 0 1709 4041 4932 5968 7123 8430 956410596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863 7 291625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 2194124137 24269 24416 24803 25154 25395 8 55 66 871 3700 11426 13221 1500116367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 258729 1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 2526225566 25668 25679 25858 25888 25915 10 7520 7690 8855 9183 14654 1669517121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 2529325403 11 48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 2303323107 23128 23990 24286 24409 24595 25802 12 12 51 3894 6539 8276 1088511644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 2546325838 13 3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 2131022547 22756 22959 24768 24814 25594 25626 25880 14 21 29 69 1448 23864601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 2443125512 25814 15 18 53 7890 9934 10063 16728 19040 19809 20825 21522 2180023582 24556 25031 25547 25562 25733 25789 25906 16 4096 4582 5766 58946517 10027 12182 13247 15207 17041 18958 20133 20505 22228 24332 2461325689 25855 25883 17 0 25 819 5539 7076 7536 7695 9532 13668 15051 1768319665 20253 21996 24136 24890 25758 25784 25807 18 34 40 44 4215 60767427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 2487325107 25644 19 1595 6216 22850 25439 20 1562 15172 19517 22362 21 750812879 24324 24496 22 6298 15839 16757 18721 23 11173 15175 19966 2119524 59 13505 16941 23793 25 2267 4830 12023 20587 26 8827 9278 1307216664 27 14419 17463 23398 25348 28 6112 16534 20423 22698 29 493 891421103 24799 30 6896 12761 13206 25873 31 2 1380 12322 21701 32 1160021306 25753 25790 33 8421 13076 14271 15401 34 9630 14112 19017 20955 35212 13932 21781 25824 36 5961 9110 16654 19636 37 58 5434 9936 12770 386575 11433 19798 39 2731 7338 20926 40 14253 18463 25404 41 21791 2480525869 42 2 11646 15850 43 6075 8586 23819 44 18435 22093 24852 45 21032368 11704 46 10925 17402 18232 47 9062 25061 25674 48 18497 20853 2340449 18606 19364 19551 50 7 1022 25543 51 6744 15481 25868 52 9081 1730525164 53 8 23701 25883 54 9680 19955 22848 55 56 4564 19121 56 559515086 25892 57 3174 17127 23183 58 19397 19817 20275 59 12561 2457125825 60 7111 9889 25865 61 19104 20189 21851 62 549 9686 25548 63 658620325 25906 64 3224 20710 21637 65 641 15215 25754 66 13484 23729 2581867 2043 7493 24246 68 16860 25230 25768 69 22047 24200 24902 70 939118040 19499 71 7855 24336 25069 72 23834 25570 25852 73 1977 8800 2575674 6671 21772 25859 75 3279 6710 24444 76 24099 25117 25820 77 555312306 25915 78 48 11107 23907 79 10832 11974 25773 80 2223 17905 2548481 16782 17135 20446 82 475 2861 3457 83 16218 22449 24362 84 1171622200 25897 85 8315 15009 22633 86 13 20480 25852 87 12352 18658 2568788 3681 14794 23703 89 30 24531 25846 90 4103 22077 24107 91 23837 2562225812 92 3627 13387 25839 93 908 5367 19388 94 0 6894 25795 95 2032223546 25181 96 8178 25260 25437 97 2449 13244 22565 98 31 18928 22741 991312 5134 14838 100 6085 13937 24220 101 66 14633 25670 102 47 2251225472 103 8867 24704 25279 104 6742 21623 22745 105 147 9948 24178 1068522 24261 24307 107 19202 22406 24609

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and M is 360, the indexes of rows where 1is located in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 17 or 18below:

TABLE 17 Index of row where 1 is located in the 0th column of the ith icolumn group 0 979 1423 4166 4609 6341 8258 10334 10548 14098 1451417051 17333 17653 17830 17990 1 2559 4025 6344 6510 9167 9728 1131214856 17104 17721 18600 18791 19079 19697 19840 2 3243 6894 7950 1053912042 13233 13938 14752 16449 16727 17025 18297 18796 19400 21577 3 32723574 6341 6722 9191 10807 10957 12531 14036 15580 16651 17007 1730919415 19845 4 155 4598 10201 10975 11086 11296 12713 15364 15978 1639517542 18164 18451 18612 20617 5 1128 1999 3926 4069 5558 6085 6337 838610693 12450 15438 16223 16370 17308 18634 6 2408 2929 3630 4357 58527329 8536 8695 10603 11003 14304 14937 15767 18402 21502 7 199 3066 64466849 8973 9536 10452 12857 13675 15913 16717 17654 19802 20115 21579 8312 870 2095 2586 5517 6196 6757 7311 7368 13046 15384 18576 20349 2142421587 9 985 1591 3248 3509 3706 3847 6174 6276 7864 9033 13618 1567516446 18355 18843 10 975 3774 4083 5825 6166 7218 7633 9657 10103 1305214240 17320 18126 19544 20208 11 1795 2005 2544 3418 6148 8051 9066 972510676 10752 11512 15171 17523 20481 21059 12 167 315 1824 2325 2640 28686070 6597 7016 8109 9815 11608 16142 17912 19625 13 1298 1896 3039 43034690 8787 12241 13600 14478 15492 16602 17115 17913 19466 20597 14 5683695 6045 6624 8131 8404 8590 9059 9246 11570 14336 18657 18941 1921821506 15 228 1889 1957 2299 3011 5074 7044 7596 7689 9534 10244 1069711691 17902 21410 16 1330 1579 1739 2234 3701 3865 5713 6677 7263 1117212143 12765 17121 20011 21436 17 303 1668 2501 4925 5778 5985 9635 1014010820 11779 11849 12058 15650 20426 20527 18 698 2484 3071 3219 40544125 5663 5939 6928 7086 8054 12173 16280 17945 19302 19 232 1619 30404901 7438 8135 9117 9233 10131 13321 17347 17436 18193 18586 19929 20 123721 6254 6609 7880 8139 10437 12262 13928 14065 14149 15032 15694 1625418883 21 482 915 1548 1637 6687 9338 10163 11768 11970 15524 15695 1738618787 19210 19340 22 1291 2500 4109 4511 5099 5194 10014 13165 1325613972 15409 16113 16214 18584 20998 23 1761 4778 7444 7740 8129 83418931 9136 9207 10003 10678 13959 17673 18194 20990 24 3060 3522 53615692 6833 8342 8792 11023 11211 11548 11914 13987 15442 15541 19707 251322 2348 2970 5632 6349 7577 8782 9113 9267 9376 12042 12943 1668016970 21321 26 6785 11960 21455 27 1223 15672 19550 28 5976 11335 2038529 2818 9387 15317 30 2763 3554 18102 31 5230 11489 18997 32 5809 1577920674 33 2620 17838 18533 34 3025 9342 9931 35 3728 5337 12142 36 25206666 9164 37 12892 15307 20912 38 10736 12393 16539 39 1075 2407 1285340 4921 5411 18206 41 5955 15647 16838 42 6384 10336 19266 43 429 1042117266 44 4880 10431 12208 45 2910 11895 12442 46 7366 18362 18772 474341 7903 14994 48 4564 6714 7378 49 4639 8652 18871 50 15787 1804820246 51 3241 11079 13640 52 1559 2936 15881 53 2737 6349 10881 54 1039416107 17073 55 8207 9043 12874 56 7805 16058 17905 57 11189 15767 1776458 5823 12923 14316 59 11080 20390 20924 60 568 8263 17411 61 1845 35576562 62 2890 10936 14756 63 9031 14220 21517 64 3529 12955 15902 65 4136750 8735 66 6784 12092 16421 67 12019 13794 15308 68 12588 15378 1767669 8067 14589 19304 70 1244 5877 6085 71 15897 19349 19993 72 1426 239412264 73 3456 8931 12075 74 13342 15273 20351 75 9138 13352 20798 767031 7626 14081 77 4280 4507 15617 78 4170 10569 14335 79 3839 751416578 80 4688 12815 18782 81 4861 7858 9435 82 605 5445 12912 83 22804734 7311 84 6668 8128 12638 85 3733 10621 19534 86 13933 18316 19341 871786 3037 21566 88 2202 13239 16432 89 4882 5808 9300 90 4580 8484 1675491 14630 17502 18269 92 6889 11119 12447 93 8162 9078 16330 94 653817851 18100 95 17763 19793 20816 96 2183 11907 17567 97 6640 14428 1517598 877 12035 14081 99 1336 6468 12328 100 5948 9146 12003 101 3782 569912445 102 1770 7946 8244 103 7384 12639 14989 104 1469 11586 20959 1057943 10450 15907 106 5005 8153 10035 107 17750 18826 21513 108 4725 804110112 109 3837 16266 17376 110 11340 17361 17512 111 1269 4611 4774 1122322 10813 16157 113 16752 16843 18959 114 70 4325 18753 115 3165 815315384 116 160 8045 16823 117 14112 16724 16792 118 4291 7667 18176 1195943 19879 20721

TABLE 18 Index of row where 1 is located in the 0th column of the ith icolumn group 0 316 1271 3692 9495 12147 12849 14928 16671 16938 1786419108 20502 21097 21115 1 2341 2559 2643 2816 2865 5137 5331 7000 75238023 10439 10797 13208 15041 2 5556 6858 7677 10162 10207 11349 1232112398 14787 15743 15859 15952 19313 20879 3 349 573 910 2702 3654 62149246 9353 10638 11772 14447 14953 16620 19888 4 204 1390 2887 3835 62306533 7443 7876 9299 10291 10896 13960 18287 20086 5 541 2429 2838 71448523 8637 10490 10585 11074 12074 15762 16812 17900 18548 6 733 16593838 5323 5805 7882 9429 10682 13697 16909 18846 19587 19592 20904 71134 2136 4631 4653 4718 5197 10410 11666 14996 15305 16048 17417 1896020303 8 734 1001 1283 4959 10016 10176 10973 11578 12051 15550 1591519022 19430 20121 9 745 4057 5855 9885 10594 10989 13156 13219 1335113631 13685 14577 17713 20386 10 968 1446 2130 2502 3092 3787 5323 81048418 9998 11681 13972 17747 17929 11 3020 3857 5275 5786 6319 8608 1194314062 17144 17752 18001 18453 19311 21414 12 709 747 1038 2181 5320 829210584 10859 13964 15009 15277 16953 20675 21509 13 1663 3247 5003 57607186 7360 10346 14211 14717 14792 15155 16128 17355 17970 14 516 5781914 6147 9419 11148 11434 13289 13325 13332 19106 19257 20962 21556 155009 5632 6531 9430 9886 10621 11765 13969 16178 16413 18110 18249 2061620759 16 457 2686 3318 4608 5620 5858 6480 7430 9602 12691 14664 1877720152 20848 17 33 2877 5334 6851 7907 8654 10688 15401 16123 17942 1796918747 18931 20224 18 87 897 7636 8663 11425 12288 12672 14199 1643517615 17950 18953 19667 20281 19 1042 1832 2545 2719 2947 3672 3700 62496398 6833 11114 14283 17694 20477 20 326 488 2662 2880 3009 5357 65878882 11604 14374 18781 19051 19057 20508 21 854 1294 2436 2852 4903 64667761 9072 9564 10321 13638 15658 16946 19119 22 194 899 1711 2408 27865391 7108 8079 8716 11453 17303 19484 20989 21389 23 1631 3121 3994 50057810 8850 10315 10589 13407 17162 18624 18758 19311 20301 24 736 24244792 5600 6370 10061 16053 16775 18600 25 1254 8163 8876 9157 1214114587 16545 17175 18191 26 388 6641 8974 10607 10716 14477 16825 1719118400 27 5578 6082 6824 7360 7745 8655 11402 11665 12428 28 3603 872913463 14698 15210 19112 19550 20727 21052 29 48 1732 3805 5158 1544216909 19854 21071 21579 30 11707 14014 21531 31 1542 4133 4925 32 1008313505 21198 33 14300 15765 16752 34 778 1237 11215 35 1325 3199 14534 362007 14510 20599 37 1996 5881 16429 38 5111 15018 15980 39 4989 1068112810 40 3763 10715 16515 41 2259 10080 15642 42 9032 11319 21305 433915 15213 20884 44 11150 15022 20201 45 1147 6749 19625 46 12139 1293918870 47 3840 4634 10244 48 1018 10231 17720 49 2708 13056 13393 50 578111588 18888 51 1345 2036 5252 52 5908 8143 15141 53 1804 13693 18640 5410433 13965 16950 55 9568 10122 15945 56 547 6722 14015 57 321 1284414095 58 2632 10513 14936 59 6369 11995 20321 60 9920 19136 21529 611990 2726 10183 62 5763 12118 15467 63 503 10006 19564 64 9839 1194219472 65 11205 13552 15389 66 8841 13797 19697 67 124 6053 18224 68 647714406 21146 69 1224 8027 16011 70 3046 4422 17717 71 739 12308 17760 724014 4130 7835 73 2266 5652 11981 74 2711 7970 18317 75 2196 15229 1721776 8636 13302 16764 77 5612 15010 16657 78 615 1249 4639 79 3821 1207318506 80 1066 16522 21536 81 11307 18363 19740 82 3240 8560 10391 833124 11424 20779 84 1604 8861 17394 85 2083 7400 8093 86 3218 7454 915587 9855 15998 20533 88 316 2850 20652 89 5583 9768 10333 90 7147 771318339 91 12607 17428 21418 92 14216 16954 18164 93 8477 15970 18488 941632 8032 9751 95 4573 9080 13507 96 11747 12441 13876 97 1183 1560516675 98 4408 10264 17109 99 5495 7882 12150 100 1010 3763 5065 101 982818054 21599 102 6342 7353 15358 103 6362 9462 19999 104 7184 13693 17622105 4343 4654 10995 106 7099 8466 18520 107 11505 14395 15138 108 677916691 18726 109 7146 12644 20196 110 5865 16728 19634 111 4657 871421246 112 4580 5279 18750 113 3767 6620 18905 114 9209 13093 17575 11512486 15875 19791 116 8046 14636 17491 117 2120 4643 13206 118 6186 967512601 119 784 5770 21585

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 11/15, and M is 360, the indexes of rows where 1is located in the 0^(th) column of the 1^(th) column group of theinformation word submatrix 210 are defined as shown in Table 19 below.

TABLE 19 Index of row where 1 is located in the 0th column of the ith icolumn group 0 696 989 1238 3091 3116 3738 4269 6406 7033 8048 915710254 12033 16456 16912 1 444 1488 6541 8626 10735 12447 13111 1370614135 15195 15947 16453 16916 17137 17268 2 401 460 992 1145 1576 16782238 2320 4280 6770 10027 12486 15363 16714 17157 3 1161 3108 3727 45085092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205 4 542 11906883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 1704017063 5 17 487 776 880 5077 6172 9771 11446 12798 16016 16109 1617117087 17132 17226 6 1337 3275 3462 4229 9246 10180 10845 10866 1225013633 14482 16024 16812 17186 17241 7 15 980 2305 3674 5971 8224 1149911752 11770 12897 14082 14836 15311 16391 17209 8 0 3926 5869 8696 93519391 11371 14052 14172 14636 14974 16619 16961 17033 17237 9 3033 53176501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 1706217090 10 981 1205 4400 6410 11003 13319 13405 14695 15846 16297 1649216563 16616 16862 16953 11 1725 4276 8869 9588 14062 14486 15474 1554816300 16432 17042 17050 17060 17175 17273 12 1807 5921 9960 10011 1430514490 14872 15852 16054 16061 16306 16799 16833 17136 17262 13 2826 47526017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 1717917247 14 1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 1601116421 16825 17112 17195 15 2890 4821 5987 7226 8823 9869 12468 1469415352 15805 16075 16462 17102 17251 17263 16 3751 3890 4382 5720 1028110411 11350 12721 13121 14127 14980 15202 15335 16735 17123 17 26 302805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 1710318 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266 19 904 3157 6284 7151 7984 11712 12887 13767 1554716099 16753 16829 17044 17250 17259 20 7 311 4876 8334 9249 11267 1407214559 15003 15235 15686 16331 17177 17238 17253 21 4410 8066 8596 963110369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204 22 248261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220 23 88 11622 14735 15890 24 304 2026 2638 6018 25 1163 426811620 17232 26 9701 11785 14463 17260 27 4118 10952 12224 17006 28 364710823 11521 12060 29 1717 3753 9199 11642 30 2187 14280 17220 31 1478716903 17061 32 381 3534 4294 33 3149 6947 8323 34 12562 16724 16881 357289 9997 15306 36 5615 13152 17260 37 5666 16926 17027 38 4190 779816831 39 4778 10629 17180 40 10001 13884 15453 41 6 2237 8203 42 783115144 15160 43 9186 17204 17243 44 9435 17168 17237 45 42 5701 17159 467812 14259 15715 47 39 4513 6658 48 38 9368 11273 49 1119 4785 17182 505620 16521 16729 51 165685 17242 52 210 3452 12383 53 466 14462 16250 5410548 12633 13962 55 1452 6005 16453 56 22 4120 13684 57 5195 1156316522 58 5518 16705 17201 59 12233 14552 15471 60 6067 13440 17248 618660 8967 17061 62 8673 12176 15051 63 5959 15767 16541 64 3244 1210912414 65 31 15913 16323 66 3270 15686 16653 67 24 7346 14675 68 12 15318740 69 6228 7565 16667 70 16936 17122 17162 71 4868 8451 13183 72 37144451 16919 73 11313 13801 17132 74 17070 17191 17242 75 1911 11201 1718676 14 17190 17254 77 11760 16008 16832 78 14543 17033 17278 79 1612916765 17155 80 6891 15561 17007 81 12741 14744 17116 82 8992 16661 1727783 1861 11130 16742 84 4822 13331 16192 85 13281 14027 14989 86 38 1488717141 87 10698 13452 15674 88 4 2539 16877 89 857 17170 17249 90 1144911906 12867 91 285 14118 16831 92 15191 17214 17242 93 39 728 16915 942469 12969 15579 95 16644 17151 17164 96 2592 8280 10448 97 9236 1243117173 98 9064 16892 17233 99 4526 16146 17038 100 31 2116 16083 10115837 16951 17031 102 5362 8382 16618 103 6137 13199 17221 104 284115068 17068 105 24 3620 17003 106 9880 15718 16764 107 1784 10240 17209108 2731 10293 10846 109 3121 8723 16598 110 8563 15662 17088 111 131167 14676 112 29 13850 15963 113 3654 7553 8114 114 23 4362 14865 1154434 14741 16688 116 8362 13901 17244 117 13687 16736 17232 118 46 422913394 119 13169 16383 16972 120 16031 16681 16952 121 3384 9894 12580122 9841 14414 16165 123 5013 17099 17115 124 2130 8941 17266 125 690715428 17241 126 16 1860 17235 127 2151 16014 16643 128 14954 15958 17222129 3969 8419 15116 130 31 15593 16984 131 11514 16605 17255

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 12/15, and M is 360, the indexes of rows where 1is located in the 0^(th) column of the 1^(th) column group of theinformation word submatrix 210 are defined as shown in Table 20 below.

TABLE 20 Index of row where 1 is located in the 0th column of the ith icolumn group 0 584 1472 1621 1867 3338 3568 3723 4185 5126 5889 77378632 8940 9725 1 221 445 590 3779 3835 6939 7743 8280 8448 8491 936710042 11242 12917 2 4662 4837 4900 5029 6449 6687 6751 8684 9936 1168111811 11886 12089 12909 3 2418 3018 3647 4210 4473 7447 7502 9490 1006711092 11139 11256 12201 12383 4 2591 2947 3349 3406 4417 4519 5176 66728498 8863 9201 11294 11376 12184 5 27 101 197 290 871 1727 3911 54116676 8701 9350 10310 10798 12439 6 1765 1897 2923 3584 3901 4048 69637054 7132 9165 10184 10824 11278 12669 7 2183 3740 4808 5217 5660 63756787 8219 8466 9037 10353 10583 11118 12762 8 73 1594 2146 2715 35013572 3639 3725 6959 7187 8406 10120 10507 10691 9 240 732 1215 2185 27882830 3499 3881 4197 4991 6425 7061 9756 10491 10 831 1568 1828 3424 43194516 4639 6018 9702 10203 10417 11240 11518 12458 11 2024 2970 3048 36383576 4152 5284 5779 5926 9426 9945 10873 11787 11837 12 1049 1218 16512328 3493 4363 5750 6483 7613 8782 9738 9803 11744 11937 13 1193 20602289 2964 3478 4592 4756 6709 7162 8231 8326 11140 11908 12243 14 9782120 2439 3338 3850 4589 6567 8745 9656 9708 10161 10542 10711 12639 152403 2938 3117 3247 3711 5593 5844 5932 7801 10152 10226 11498 1216212941 16 1781 2229 2276 2533 3582 3951 5279 5774 7930 9824 10920 1103812340 12440 17 289 384 1980 2230 3464 3873 5958 8656 8942 9006 1017511425 11745 12530 18 155 354 1090 1330 2002 2236 3559 3705 4922 59586576 8564 9972 12760 19 303 876 2059 2142 5244 5330 6644 7576 8614 959810410 10718 11033 12957 20 3449 3617 4408 4602 4727 6182 8835 8928 93729644 10237 10747 11655 12747 21 811 2565 2820 8677 8974 9632 11069 1154811839 12107 12411 12695 12812 12890 22 972 4123 4943 6385 6449 7339 74778379 9177 9359 10074 11709 12552 12831 23 842 973 1541 2262 2905 52766758 7099 7894 8128 8325 8663 8875 10050 24 474 791 968 3902 4924 49655085 5908 6109 6329 7931 9038 9401 10568 25 1397 4461 4658 5911 60377127 7318 8678 8924 9000 9473 9602 10446 12692 26 1334 7571 12881 271393 1447 7972 28 633 1257 10597 29 4843 5102 11056 30 3294 8015 1051331 1108 10374 10546 32 5353 7824 10111 33 3398 7674 8569 34 7719 947810503 35 2997 9418 9581 36 5777 6519 11229 37 1966 5214 9899 38 6 40885827 39 836 9248 9612 40 483 7229 7548 41 7865 8289 9804 42 2915 1109811900 43 6180 7096 9481 44 1431 6786 8924 45 748 6757 8625 46 3312 44757204 47 1852 8958 11020 48 1915 2903 4006 49 6776 10886 12531 50 25949998 12742 51 159 2002 12079 52 853 3281 3762 53 5201 5798 6413 54 38826062 12047 55 4133 6775 9657 56 228 6874 11183 57 7433 10728 10864 587735 8073 12734 59 2844 4621 11779 60 3909 7103 12804 61 6002 9704 1106062 5864 6856 7681 63 3652 5869 7605 64 2546 2657 4461 65 2423 4203 911166 244 1855 4691 67 1106 2178 6371 68 391 1617 10126 69 250 9259 1060370 3435 4614 6924 71 1742 8045 9529 72 7667 8875 11451 73 4023 6108 691174 8621 10184 11650 75 6726 10861 12348 76 3228 6302 7388 77 1 1137 535878 381 2424 8537 79 3256 7508 10044 80 1980 2219 4569 81 2468 5699 1031982 2803 3314 12808 83 8578 9642 11533 84 829 4585 7923 85 59 329 5575 861067 5709 6867 87 1175 4744 12219 88 109 2518 6756 89 2105 10626 1115390 5192 10696 10749 91 6260 7641 8233 92 2998 3094 11214 93 3398 646611494 94 6574 10448 12160 95 2734 10755 12780 96 1028 7958 10825 97 85458602 10793 98 392 3398 11417 99 6639 9291 12571 100 1067 7919 8934 1011064 2848 12753 102 6076 8656 12690 103 5504 6193 10171 104 1951 71567356 105 4389 4780 7889 106 526 4804 9141 107 1238 3648 10464 108 25875624 12557 109 5560 5903 11963 110 1134 2570 3297 111 10041 11583 12157112 1263 9585 12912 113 3744 7898 10646 114 45 9074 10315 115 1051 618810038 116 2242 8394 12712 117 3598 9025 12651 118 2295 3540 5610 1191914 4378 12423 120 1766 3635 12759 121 5177 9586 11143 122 943 359011649 123 4864 6905 10454 124 5852 6042 10421 125 6095 8285 12349 1262070 7171 8563 127 718 12234 12716 128 512 10667 11353 129 3629 64857040 130 2880 8865 11466 131 4490 10220 11796 132 5440 8819 9103 1335262 7543 12411 134 516 7779 10940 135 2515 5843 9202 136 4684 599410586 137 573 2270 3324 138 7870 8317 10322 139 6856 7638 12909 140 15837669 10781 141 8141 9085 12555 142 3903 5485 9992 143 4467 11998 12904

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 13/15, and M is 360, the indexes of rows where 1exists in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 21 below:

TABLE 21 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 142 2307 2598 2650 4028 4434 5781 5881 6016 6323 66816698 8125 1 2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 85398583 2 899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602 321 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616 4 20 17452838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631 5 9 6274 67256792 7195 7333 8027 8186 8209 8273 8442 8548 8632 6 494 1365 2405 37995188 5291 7644 7926 8139 8458 8504 8594 8625 7 192 574 1179 4387 46955089 5831 7673 7789 8298 8301 8612 8632 8 11 20 1406 6111 6176 6256 67086834 7828 8232 8457 8495 8602 9 6 2654 3554 4483 4966 5866 6795 80698249 8301 8497 8509 8623 10 21 1144 2355 3124 6773 6805 6887 7742 79948358 8374 8580 8611 11 335 4473 4883 5528 6096 7543 7586 7921 8197 83198394 8489 8636 12 2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 85448586 8617 13 12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 813714 710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619 15200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526 16 32501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636 17 3062 45995885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598 18 105 381 15744351 5452 5603 5943 7467 7788 7933 8362 8513 8587 19 787 1857 3386 36596550 7131 7965 8015 8040 8312 8484 8525 8537 20 15 1118 4226 5197 55755761 6762 7038 8260 8338 8444 8512 8568 21 36 5216 5368 5616 6029 65918038 8067 8299 8351 8565 8578 8585 22 1 23 4300 4530 5426 5532 5817 69677124 7979 8022 8270 8437 23 629 2133 4828 5475 5875 5890 7194 8042 83458385 8518 8598 8612 24 11 1065 3782 4237 4993 7104 7863 7904 8104 82288321 8383 8565 25 2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 85278557 8614 26 5600 6591 7491 7696 27 1766 8281 8626 28 1725 2280 5120 291650 3445 7652 30 4312 6911 8626 31 15 1013 5892 32 2263 2546 2979 331545 5873 7406 34 67 726 3697 35 2860 6443 8542 36 17 911 2820 37 15614580 6052 38 79 5269 7134 39 22 2410 2424 40 3501 5642 8627 41 808 69508571 42 4099 6389 7482 43 4023 5000 7833 44 5476 5765 7917 45 1008 31947207 46 20 495 5411 47 1703 8388 8635 48 6 4395 4921 49 200 2053 8206 501089 5126 5562 51 10 4193 7720 52 1967 2151 4608 53 22 738 3513 54 33855066 8152 55 440 1118 8537 56 3429 6058 7716 57 5213 7519 8382 58 55648365 8620 59 43 3219 8603 60 4 5409 5815 61 5 6376 7654 62 4091 57245953 63 5348 6754 8613 64 1634 6398 6632 65 72 2058 8605 66 3497 58117579 67 3846 6743 8559 68 15 5933 8629 69 2133 5859 7068 70 4151 46178566 71 2960 8270 8410 72 2059 3617 8210 73 544 1441 6895 74 4043 74828592 75 294 2180 8524 76 3058 8227 8373 77 364 5756 8617 78 5383 85558619 79 1704 2480 4181 80 7338 7929 7990 81 2615 3905 7981 82 4298 45488296 83 8262 8319 8630 84 892 1893 8028 85 5694 7237 8595 86 1487 50125810 87 4335 8593 8624 88 3509 4531 5273 89 10 22 830 90 4161 5208 628091 275 7063 8634 92 4 2725 3113 93 2279 7403 8174 94 1637 3328 3930 952810 4939 5624 96 3 1234 7687 97 2799 7740 8616 98 22 7701 8636 99 43027857 7993 100 7477 7794 8592 101 9 6111 8591 102 5 8606 8628 103 3473497 4033 104 1747 2613 8636 105 1827 5600 7042 106 580 1822 6842 107232 7134 7783 108 4629 5000 7231 109 951 2806 4947 110 571 3474 8577 1112437 2496 7945 112 23 5873 8162 113 12 1168 7686 114 8315 8540 8596 1151766 2506 4733 116 929 1516 3338 117 21 1216 6555 118 782 1452 8617 1198 6083 6087 120 667 3240 4583 121 4030 4661 5790 122 559 7122 8553 1233202 4388 4909 124 2533 3673 8594 125 1991 3954 6206 126 6835 7900 7980127 189 5722 8573 128 2680 4928 4998 129 243 2579 7735 130 4281 81328566 131 7656 7671 8609 132 1116 2291 4166 133 21 388 8021 134 6 11238369 135 311 4918 8511 136 0 3248 6290 137 13 6762 7172 138 4209 56327563 139 49 127 8074 140 581 1735 4075 141 0 2235 5470 142 2178 58206179 143 16 3575 6054 144 1095 4564 6458 145 9 1581 5953 146 2537 64698552 147 14 3874 4844 148 0 3269 3551 149 2114 7372 7926 150 1875 23884057 151 3232 4042 6663 152 9 401 583 153 13 4100 6584 154 2299 41904410 155 21 3670 4979

According to an exemplary embodiment, even when the order of numbers ina sequence corresponding to the i^(th) column group of the parity checkmatrix 200 as shown in the above-described Tables 4 to 21 is changed,the changed parity check matrix is a parity check matrix used for thesame code. Therefore, a case in which the order of numbers in thesequence corresponding to the i^(th) column group in Tables 4 to 21 ischanged is covered by the inventive concept.

According to an exemplary embodiment, even when the arrangement order ofsequences corresponding to each column group is changed in Tables 4 to21, cycle characteristics on a graph of a code and algebraiccharacteristics such as degree distribution are not changed. Therefore,a case in which the arrangement order of the sequences shown in Tables 4to 21 is changed is also covered by the inventive concept.

In addition, even when a multiple of Q_(ldpc) is equally added to allsequences corresponding to a certain column group in Tables 4 to 21, thecycle characteristics on the graph of the code or the algebraiccharacteristics such as degree distribution are not changed. Therefore,a result of equally adding a multiple of Q_(ldpc) to the sequences shownin Tables 4 to 21 is also covered by the inventive concept. However, itshould be noted that, when the resulting value obtained by adding themultiple of Q_(ldpc) to a given sequence is greater than or equal to(N_(ldpc)−K_(ldpc)), a value obtained by applying a modulo operation for(N_(ldpc)−K_(ldpc)) to the resulting value should be applied instead.

Once positions of the rows where 1 exists in the 0^(th) column of thei^(th) column group of the information word submatrix 210 are defined asshown in Tables 4 to 21, positions of rows where 1 exists in anothercolumn of each column group may be defined since the positions of therows where 1 exists in the 0^(th) column are cyclic-shifted by Q_(ldpc)in the next column.

For example, in the case of Table 4, in the 0^(th) column of the 0^(th)column group of the information word submatrix 210, 1 exists in the245^(th) row, 449^(th) row, 491^(st) row, . . . .

In this case, since Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M=(16200−5400)/360=30,the indexes of the rows where 1 is located in the 1^(st) column of the0^(th) column group may be 275(=245+30), 479(=449+30), 521(=491+30), . .. , and the indexes of the rows where 1 is located in the 2^(nd) columnof the 0^(th) column group may be 305(=275+30), 509(=479+30),551(=521+30), . . . .

In the above-described method, the indexes of the rows where 1 islocated in all rows of each column group may be defined.

The parity submatrix 220 of the parity check matrix 200 shown in FIG. 2may be defined as follows:

The parity submatrix 220 includes N_(ldpc)−K_(ldpc) number of columns(that is, K_(ldpc) ^(th) column to (N_(lpdc)−1)^(th) column), and has adual diagonal or staircase configuration. Accordingly, the degree ofcolumns except the last column (that is, (N_(ldpc)−1)^(th) column) fromamong the columns included in the parity submatrix 220 is 2, and thedegree of the last column is 1.

As a result, the information word submatrix 210 of the parity checkmatrix 200 may be defined by Tables 4 to 21, and the parity submatrix220 of the parity check matrix 200 may have a dual diagonalconfiguration.

When the columns and rows of the parity check matrix 200 shown in FIG. 2are permutated based on Equation 4 and Equation 5, the parity checkmatrix shown in FIG. 2 may be changed to a parity check matrix 300 shownin FIG. 3.

Q _(ldpc) ·i+j⇒M·j+i(0≤i<M,0≤j<Q _(ldpc))  (4)

K _(ldpc) +Q _(ldpc) ·k+l⇒K _(ldpc) +M·l+k(0≤k<M,0≤l<Q _(ldpc))  (5)

The method for permutating based on Equation 4 and Equation 5 will beexplained below. Since row permutation and column permutation apply thesame principle, the row permutation will be explained by the way of anexample.

In the case of the row permutation, regarding the X^(th) row, i and jsatisfying X=Q_(ldpc)×i+j are calculated and the X^(th) row ispermutated by assigning the calculated i and j to M×j+i. For example,regarding the 7^(th) row, i and j satisfying 7=2×i+j are 3 and 1,respectively. Therefore, the 7^(th) row is permutated to the 13^(th) row(10×1+3=13).

When the row permutation and the column permutation are performed in theabove-described method, the parity check matrix of FIG. 2 may beconverted into the parity check matrix of FIG. 3.

Referring to FIG. 3, the parity check matrix 300 is divided into aplurality of partial blocks, and a quasi-cyclic matrix of M×Mcorresponds to each partial block.

Accordingly, the parity check matrix 300 having the configuration ofFIG. 3 is formed of matrix units of M×M. That is, the submatrices of M×Mare arranged in the plurality of partial blocks, constituting the paritycheck matrix 300.

Since the parity check matrix 300 is formed of the quasi-cyclic matricesof M×M, M number of columns may be referred to as a column block and Mnumber of rows may be referred to as a row block. Accordingly, theparity check matrix 300 having the configuration of FIG. 3 is formed ofN_(qc) _(_) _(column)=N_(ldpc)/M number of column blocks and N_(qc) _(_)_(row)=N_(parity)/M number of row blocks.

Hereinafter, the submatrix of M×M will be explained.

First, the (N_(qc) _(_) _(column)−1)^(th) column block of the 0^(th) rowblock has a form shown in Equation 6 presented below:

$\begin{matrix}{A = \begin{bmatrix}0 & 0 & \ldots & 0 & 0 \\1 & 0 & \ldots & 0 & 0 \\0 & 1 & \ldots & 0 & 0 \\M & M & M & M & M \\0 & 0 & \ldots & 1 & 0\end{bmatrix}} & (6)\end{matrix}$

As described above, A 330 is an M×M matrix, values of the 0^(th) row andthe (M−1)^(th) column are all “0”, and, regarding 0≤i≤(M−2), the(i+1)^(th) row of the i^(th) column is “1” and the other values are “0”.

Second, regarding 0≤i≤(N_(ldpc)−K_(ldpc))/M−1 in the parity submatrix320, the i^(th) row block of the (K_(ldpc)/M+i)^(th) column block isconfigured by a unit matrix I_(M×M) 340. In addition, regarding0≤i≤(N_(ldpc)−K_(ldpc))/M−2, the (i+1)^(th) row block of the(K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M)340.

Third, a block 350 constituting the information word submatrix 310 mayhave a cyclic-shifted format of a cyclic matrix P, P^(a) ^(ij) , or anadded format of the cyclic-shifted matrix P^(a) ^(ij) of the cyclicmatrix P (or an overlapping format).

For example, a format in which the cyclic matrix P is cyclic-shifted tothe right by 1 may be expressed by Equation 7 presented below:

$\begin{matrix}{P = \begin{bmatrix}0 & 1 & 0 & \; & 0 \\0 & 0 & 1 & \Lambda & 0 \\M & M & M & \; & M \\0 & 0 & 0 & \Lambda & 1 \\1 & 0 & 0 & \; & 0\end{bmatrix}} & (7)\end{matrix}$

The cyclic matrix P is a square matrix having an M×M size and is amatrix in which a weight of each of M number of rows is 1 and a weightof each of M number of columns is 1. When a_(ij) is 0, the cyclic matrixP, that is, P⁰ indicates a unit matrix I_(M×M), and when a_(ij) is ∞,P^(∞) is a zero matrix.

A submatrix existing where the i^(th) row block and the j^(th) columnblock intersect in the parity check matrix 300 of FIG. 3 may be P^(a)^(ij) . Accordingly, i and j indicate the number of row blocks and thenumber of column blocks in the partial blocks corresponding to theinformation word. Accordingly, in the parity check matrix 300, the totalnumber of columns is N_(ldpc)=M×N_(qc) _(_) _(column), and the totalnumber of rows is N_(parity)=M×N_(qc) _(_) _(row). That is, the paritycheck matrix 300 is formed of N_(qc) _(_) _(column) number of “columnblocks” and N_(qc) _(_) _(row) number of “row blocks”.

Hereinafter, a method for performing LDPC encoding based on the paritycheck matrix 200 as shown in FIG. 2 will be explained. An LDPC encodingprocess when the parity check matrix 200 is defined as shown in Table 10by way of an example will be explained for the convenience ofexplanation.

First, when information word bits having a length of K_(ldpc) are [i₀,i₁, i₂, . . . , i_(K) _(ldp) ₋₁], and parity bits having a length ofN_(ldpc)−K_(ldpc) are [p₀, p₁, p₂, . . . p_(N) _(ldpc) _(-K) _(ldpc)₋₁], the LDPC encoding is performed by the following process.

Step 1) Parity bits are initialized as ‘0’. That is, p₀=p₁=p₂= . . .=p_(N) _(ldpc) _(-K) _(ldpc) ₋₁=0.

Step 2) The 0^(th) information word bit i₀ is accumulated in a paritybit having the address of the parity bit defined in the first row (thatis, the row of i=0) of Table 10 as the index of the parity bit. This maybe expressed by Equation 8 presented below:

$\begin{matrix}{{P_{49} = {P_{49} \oplus i_{0}}}{P_{719} = {P_{719} \oplus i_{0}}}{P_{784} = {P_{784} \oplus i_{0}}}{P_{794} = {P_{794} \oplus i_{0}}}{P_{968} = {P_{968} \oplus i_{0}}}{P_{2382} = {P_{2382} \oplus i_{0}}}{P_{2685} = {P_{2685} \oplus i_{0}}}{P_{2873} = {P_{2873} \oplus i_{0}}}{P_{2974} = {P_{2974} \oplus i_{0}}}{P_{2995} = {P_{2995} \oplus i_{0}}}{P_{3540} = {P_{3540} \oplus i_{0}}}{P_{4179} = {P_{4179} \oplus i_{0}}}} & (8)\end{matrix}$

Herein, i₀ is a 0^(th) information word bit, p_(i) is an ith parity bit,and ⊕ is a binary operation. According to the binary operation, 1 ⊕1equals 0, 1β0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 3) The other 359 information word bits i_(m) (m=1, 2, . . . , 359)are accumulated in the parity bit. The other information word bits maybelong to the same column group as that of i₀. In this case, the addressof the parity bit may be determined based on Equation 9 presented below:

(x+(m mod 360)×Q _(ldpc))mod(N _(ldpc) −K _(ldpc))  (9)

Herein, x is an address of a parity bit accumulator corresponding to theinformation word bit i₀, and Q_(ldpc) is a size by which each column iscyclic-shifted in the information word submatrix, and may be 12 in thecase of Table 10. In addition, since m=1, 2, . . . , 359, (m mod 360) inEquation 9 may be regarded as m.

As a result, information word bits i_(m) (m=1, 2, . . . , 359) areaccumulated in the parity bits having the address of the parity bitcalculated based on Equation 9 as the index. For example, an operationas shown in Equation 10 presented below may be performed for theinformation word bit i₁:

$\begin{matrix}{{P_{61} = {P_{61} \oplus i_{1}}}{P_{731} = {P_{731} \oplus i_{1}}}{P_{796} = {P_{796} \oplus i_{1}}}{P_{806} = {P_{806} \oplus i_{1}}}{P_{980} = {P_{980} \oplus i_{1}}}{P_{2394} = {P_{2394} \oplus i_{1}}}{P_{2697} = {P_{2697} \oplus i_{1}}}{P_{2885} = {P_{2885} \oplus i_{1}}}{P_{2986} = {P_{2986} \oplus i_{1}}}{P_{3007} = {P_{3007} \oplus i_{1}}}{P_{3552} = {P_{3552} \oplus i_{1}}}{P_{4191} = {P_{4191} \oplus i_{1}}}} & (10)\end{matrix}$

Herein, i₁ is a 1^(st) information word bit, p_(i) is an ith parity bit,and ⊕ is a binary operation. According to the binary operation, 1⊕1equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 4) The 360^(th) information word bits i₃₆₀ is accumulated in aparity bit having the address of the parity bit defined in the 2^(nd)row (that is, the row of i=1) of Table 10 as the index of the paritybit.

Step 5) The other 359 information word bits belonging to the same groupas that of the information word bit i₃₆₀ are accumulated in the paritybit. In this case, the address of the parity bit may be determined basedon Equation 9. However, in this case, x is the address of the parity bitaccumulator corresponding to the information word bit i₃₆₀.

Step 6) Steps 4 and 5 described above are repeated for all of the columngroups of Table 10.

Step 7) As a result, a parity bit p_(i) is calculated based on Equation11 presented below. In this case, i is initialized as 1.

p _(i) =p _(i) ⊕p _(i-1) i=1,2, . . . ,N _(ldpc) −K _(ldpc)−1  (11)

In Equation 11, p₁ is an ith parity bit, N_(ldpc) is a length of an LDPCcodeword, K_(ldpc), is a length of an information word of the LDPCcodeword, and ⊕ is a binary operation.

As a result, the encoder 110 may calculate the parity bits according tothe above-described method.

In another example, a parity check matrix according to an exemplaryembodiment may have a configuration as shown in FIG. 4.

Referring to FIG. 4, the parity check matrix 400 may be formed of 5matrices A, B, C, Z, and D. Hereinafter, the configuration of eachmatrix will be explained to explain the configuration of the paritycheck matrix 400.

First, M₁, M₂, Q₁, and Q₂, which are parameter values related to theparity check matrix 400 as shown in FIG. 4, may be defined as shown inTable 22 presented below according to the length and the code rate ofthe LDPC codeword.

TABLE 22 Sizes Rate Length M₁ M₂ Q₁ Q₂ 1/15 16200 2520 12600 7 35 648001080 59400 3 165 2/15 16200 3240 10800 9 30 64800 1800 54360 5 151 3/1516200 1080 11880 3 33 64800 1800 50040 5 139 4/15 16200 1080 10800 3 3064800 1800 45720 5 127 5/15 16200 720 10080 2 28 64800 1440 41760 4 1166/15 16200 1080 8640 3 24 64800 1080 37800 3 105

The matrix A is formed of K number of columns and g number of rows, andthe matrix C is formed of K+g number of columns and N−K−g number ofrows. Herein, K is a length of information word bits, and N is a lengthof the LDPC codeword.

Indexes of rows where 1 is located in the 0^(th) column of the ithcolumn group in the matrix A and the matrix C may be defined based onTables 23 to 31 according to the length and the code rate of the LDPCcodeword. In this case, an interval at which a pattern of a column isrepeated in each of the matrix A and the matrix C, that is, the numberof columns belonging to the same group, may be 360.

For example, when the length N of the LDPC codeword is 64800 and thecode rate is 3/15, the indexes of rows where 1 is located in the 0^(th)column of the ith column group in the matrix A and the matrix C aredefined as shown in Table 23 presented below:

TABLE 23 i Index of row where 1 is located in the 0th column of the ithcolumn group 0 920 963 1307 2648 6529 17455 18883 19848 19909 2414924249 38395 41589 48032 50313 1 297 736 744 5951 8438 9881 15522 1646223036 25071 34915 41193 42975 43412 49612 2 10 223 879 4662 6400 869114561 16626 17408 22810 31795 32580 43639 45223 47511 3 629 842 16663150 7596 9465 12327 18649 19052 19279 29743 30197 40106 48371 51155 4857 953 1116 8725 8726 10508 17112 21007 30649 32113 36962 39254 4663649599 50099 5 700 894 1128 5527 6216 15123 21510 24584 29026 31416 3715838460 42511 46932 51832 6 430 592 1521 3018 10430 18090 18092 1838820017 34383 35006 38255 41700 42158 45211 7 91 1485 1733 11624 1296917531 21324 23657 27148 27509 28753 35093 43352 48104 51648 8 18 34 1176739 8679 11018 12163 16733 24113 25906 30605 32700 36465 40799 43359 9481 1545 1644 4216 4606 6015 6609 14659 16966 18056 19137 26670 2800130668 49061 10 174 1208 1387 10580 11507 13751 16344 22735 23559 2649227672 33399 44787 44842 45992 11 1151 1185 1472 6727 10701 14755 1568817441 21281 23692 23994 31366 35854 37301 43148 12 200 799 1583 34515880 7604 8194 13428 16109 18584 20463 22373 31977 47073 50087 13 346843 1352 13409 17376 18233 19119 19382 20578 24183 32052 32912 4320448539 49893 14 76 457 1169 13516 14520 14638 22391 25294 31067 3132536711 44072 44854 49274 51624 15 759 798 1420 6661 12101 12573 1379615510 18384 26649 30875 36856 38994 43634 49281 16 551 797 1000 399910040 11246 15793 23298 23822 38480 39209 45334 46603 46625 47633 17 441875 1554 5336 25948 28842 30329 31503 39203 39673 46250 47021 4855549229 51421 18 963 1470 1642 3180 3943 6513 9125 15641 17083 18876 2849932764 42420 43922 45762 19 293 324 867 8803 10582 17926 19830 2249724848 30034 34659 37721 41523 42534 47806 20 687 975 1356 2721 3002 38744119 12336 17119 21251 22482 22833 24681 26225 48514 21 549 951 12689144 11710 12623 18949 19362 22769 32603 34559 34683 36338 47140 5106922 52 890 1669 3905 5670 14712 18314 22297 30328 33389 35447 35512 3551640587 41918 23 656 1063 1694 3338 3793 4513 6009 7441 13393 20920 2650127576 29623 31261 42093 24 425 1018 1086 9226 10024 17552 24714 2487725853 28918 30945 31205 33103 42564 47214 25 32 1145 1438 4916 494514830 17505 19919 24118 28506 30173 31754 34230 48608 50291 26 559 12161272 2856 8703 9371 9708 16180 19127 24337 26390 36649 41105 42988 4409627 362 658 1191 7769 8998 14068 15921 18471 18780 31995 32798 3286437293 39468 44308 28 1136 1389 1785 8800 12541 14723 15210 15859 2656930127 31357 32898 38760 50523 51715 29 44 80 1368 2010 2228 6614 67679275 25237 30208 39537 42041 49906 50701 51199 30 1522 1536 1765 39145350 10869 12278 12886 16379 22743 23987 26306 30966 33854 41356 31 212648 709 3443 7007 7545 12484 13358 17008 20433 25862 31945 39207 3975240313 32 789 1062 1431 12280 17415 18098 23729 37278 38454 38763 4103944600 50700 51139 51696 33 825 1298 1391 4882 12738 17569 19177 1989627401 37041 39181 39199 41832 43636 45775 34 992 1053 1485 3806 1692918596 22017 23435 23932 30211 30390 34469 37213 46220 49646 35 771 8501039 5180 7653 13547 17980 23365 25318 34374 36115 38753 42993 4969651031 36 7383 14780 15959 18921 22579 28612 32038 36727 40851 4194742707 50480 37 8733 9464 13148 13899 19396 22933 23039 25047 29938 3358833796 48930 38 2493 12555 16706 23905 35400 36330 37065 38866 4030543807 43917 50621 39 6437 11927 14542 16617 17317 17755 18832 2477229273 31136 36925 46663 40 2191 3431 6288 6430 9908 13069 23014 2482229818 39914 46010 47246

In another example, when the length N of the LDPC codeword is 16200 andthe code rate is 4/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 24 presented below:

TABLE 24 Indexes of rows where 1 is located in the i 0th column of theith column group 0 19 585 710 3241 3276 3648 6345 9224 9890 10841 1 181494 894 2562 3201 4382 5130 5308 6493 10135 2 150 569 919 1427 2347 44757857 8904 9903 3 1005 1018 1025 2933 3280 3946 4049 4166 5209 4 420 554778 6908 7959 8344 8462 10912 11099 5 231 506 859 4478 4957 7664 77317908 8980 6 179 537 979 3717 5092 6315 6883 9353 9935 7 147 205 830 36093720 4667 7441 10196 11809 8 60 1021 1061 1554 4918 5690 6184 7986 112969 145 719 768 2290 2919 7272 8561 9145 10233 10 388 590 852 1579 16981974 9747 10192 10255 11 231 343 485 1546 3155 4829 7710 10394 11336 124381 5398 5987 9123 10365 11018 11153 13 2381 5196 6613 6844 7357 873211082 14 1730 4599 5693 6318 7626 9231 10663

In another example, when the length N of the LDPC codeword is 64800 andthe code rate is 4/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 25 presented below:

TABLE 25 Index of row where 1 is located in the i 0th column of the ithcolumn group 0 276 1754 1780 3597 8549 15196 26305 27003 33883 3718941042 41849 42356 1 730 873 927 9310 9867 17594 21969 25106 25922 3116735434 37742 45866 2 925 1202 1564 2575 2831 2951 5193 13096 18363 2059233786 34090 40900 3 973 1045 1071 8545 8980 11983 18649 21323 2278922843 26821 36720 37856 4 402 1038 1689 2466 2893 13474 15710 2413729709 30451 35568 35965 46436 5 263 271 395 5089 5645 15488 16314 2877829729 34350 34533 39608 45371 6 387 1059 1306 1955 6990 20001 2460628167 33802 35181 38481 38688 45140 7 53 851 1750 3493 11415 18882 2024423411 28715 30722 36487 38019 45416 8 810 1044 1772 3906 5832 1679317333 17910 23946 29650 34190 40673 45828 9 97 491 948 12156 13788 2497033774 37539 39750 39820 41195 46464 46820 10 192 899 1283 3732 731013637 13810 19005 24227 26772 31273 37665 44005 11 424 531 1300 48608983 10137 16323 16888 17933 22458 26917 27835 37931 12 130 279 731 30246378 18838 19746 21007 22825 23109 28644 32048 34667 13 938 1041 14829589 10065 11535 17477 25816 27966 35022 35025 42536 14 170 454 13125326 6765 23408 24090 26072 33037 38088 42985 46413 15 220 804 843 29214841 7760 8303 11259 21058 21276 34346 37604 16 676 713 832 11937 1200612309 16329 26438 34214 37471 38179 42420 17 714 931 1580 6837 982411257 15556 26730 32053 34461 35889 45821 18 28 1097 1340 8767 940617253 29558 32857 37856 38593 41781 47101 19 158 722 754 14489 2385128160 30371 30579 34963 44216 46462 47463 20 833 1326 1332 7032 956611011 21424 26827 29789 31699 32876 37498 21 251 504 1075 4470 773611242 20397 32719 34453 36571 40344 46341 22 330 581 868 15168 2026526354 33624 35134 38609 44965 45209 46909 23 729 1643 1732 3946 49129615 19699 30993 33658 38712 39424 46799 24 546 982 1274 9264 1101711868 15674 16277 19204 28606 39063 43331 25 73 1160 1196 4334 1256013583 14703 18270 18719 19327 38985 46779 26 1147 1625 1759 3767 591211599 18561 19330 29619 33671 43346 44098 27 104 1507 1586 9387 1789023532 27008 27861 30966 33579 35541 39801 28 1700 1746 1793 4941 781413746 20375 27441 30262 30392 35385 42848 29 183 555 1029 3090 5412 814819662 23312 23933 28179 29962 35514 30 891 908 1127 2827 4077 4376 457026923 274556 33699 43431 46071 31 404 1110 1782 6003 14452 19247 2699830137 31404 31624 46621 47366 32 886 1627 1704 8193 8980 9648 1092816267 19774 35111 38545 44735 33 268 380 1214 4797 5168 9109 9288 1799221309 33210 36210 41429 34 572 1121 1165 6944 7114 20978 23540 2586326190 26365 41521 44690 35 18 185 496 5885 6165 20468 23895 24745 3122633680 37665 38587 36 289 527 1118 11275 12015 18088 22805 24679 2826230160 34892 43212 37 658 926 1589 7634 16231 22193 25320 26057 2651227498 29472 34219 38 337 801 1525 2023 3512 16031 26911 32719 3562039035 43779 44316 39 248 534 670 6217 11430 24090 26509 28712 3307333912 38048 39813 40 82 1556 1575 7879 7892 14714 22404 22773 2553134170 38203 38254 41 247 313 1224 3694 14304 24033 26394 28101 3745537859 38997 41344 42 790 887 1418 2811 3288 9049 9704 13303 14262 3814940109 40477 43 1310 1384 1471 3716 8250 25371 26329 26997 30138 4084241041 44921 44 86 288 367 1860 8713 18211 22628 22811 28342 28463 4041545845 45 719 1438 1741 8258 10797 29270 29404 32096 34433 34616 3603045597 46 215 1182 1364 8146 9949 10498 18603 19304 19803 23685 4330445121 47 1243 1496 1537 8484 8851 16589 17665 20152 24283 28993 3427439795 48 6320 6785 15841 16309 20512 25804 27421 28941 43871 44647 492207 2713 4450 12217 16506 21188 23933 28789 38099 42392 50 14064 1430714599 14866 17540 18881 21065 25823 30341 36963 51 14259 14396 1703726769 29219 29319 31689 33013 35631 37319 52 7798 10495 12868 1429817221 23344 31908 39809 41001 41965

In another example, when the length N of the LDPC codeword is 16200 andthe code rate is 5/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 26 presented below:

TABLE 26 Index of rows where 1 is located in the i 0th column of the ithcolumn group 0 69 244 706 5145 5994 6066 6763 6815 8509 1 257 541 6183933 6188 7048 7484 8424 9104 2 69 500 536 1494 1669 7075 7553 820210305 3 11 189 340 2103 3199 6775 7471 7918 10530 4 333 400 434 18063264 5693 8534 9274 10344 5 111 129 260 3562 3676 3680 3809 5169 73088280 6 100 303 342 3133 3952 4226 4713 5053 5717 9931 7 83 87 374 8282460 4943 6311 8657 9272 9571 8 114 166 325 2680 4698 7703 7886 87919978 10684 9 281 542 549 1671 3178 3955 7153 7432 9052 10219 10 202 271608 3860 4173 4203 5169 6871 8113 9757 11 16 359 419 3333 4198 4737 61707987 9573 10095 12 235 244 584 4640 5007 5563 6029 6816 7678 9968 13 123449 646 2460 3845 4161 6610 7245 7686 8651 14 136 231 468 835 2622 32925158 5294 6584 9926 15 3085 4683 8191 9027 9922 9928 10550 16 2462 31853976 4091 8089 8772 9342

In another example, when the length N of the LDPC codeword is 64800 andthe code rate is 6/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 27 presented below:

TABLE 27 Indexes of rows where 1 is located in i the 0th column of theith column group 0 221 1011 1218 4299 7143 8728 11072 15533 17356 3390936833 1 360 1210 1375 2313 3493 16822 21373 23588 23656 26267 34098 2544 1347 1433 2457 9186 10945 13583 14858 19195 34606 37441 3 37 596 7154134 8091 12106 24307 24658 34108 40591 42883 4 235 398 1204 2075 674211670 13512 23231 24784 27915 34752 5 204 873 890 13550 16570 1977434012 35249 37655 39885 42890 6 221 371 514 11984 14972 15690 2882729069 30531 31018 43121 7 280 549 1435 1889 3310 10234 11575 15243 2074830469 36005 8 223 666 1248 13304 14433 14732 18943 21248 23127 3852939272 9 370 819 1065 9461 10319 25294 31958 33542 37458 39681 40039 10585 870 1028 5087 5216 12228 16216 16381 16937 27132 27893 11 164 1671210 7386 11151 20413 22713 23134 24188 36771 38992 12 298 511 809 46207347 8873 19602 24162 29198 34304 41145 13 105 830 1212 2415 14759 1544016361 16748 22123 32684 42575 14 659 665 668 6458 22130 25972 3069731074 32048 36078 37129 15 91 808 953 8015 8988 13492 13987 15979 2835534509 39698 16 594 983 1265 3028 4029 9366 11069 11512 27066 40939 4163917 506 740 1321 1484 10747 16376 17384 20285 31502 38925 42606 18 338356 975 2022 3578 18689 18772 19826 22914 24733 27431 19 709 1264 13664617 8893 25226 27800 29080 30277 37781 39644 20 840 1179 1338 2973 35417043 12712 15005 17149 19910 36795 21 1009 1267 1380 4919 12679 2288979638 30987 34637 36232 37284 22 466 913 1247 1646 3049 5924 9014 2053934546 35029 36540 23 374 697 984 1654 5870 10883 11684 20294 28888 3161234031 24 117 240 635 5093 8673 11323 12456 14145 21397 39619 42559 25122 1265 1427 13528 14282 15241 16852 17227 34723 36836 39791 26 5951180 1310 6952 17916 24725 24971 27243 29555 32138 35987 27 140 470 101713222 13253 18462 20806 21117 28673 31598 37235 28 7 710 1072 8014 1080413303 14292 16690 26676 36443 41966 29 48 189 759 12438 14523 1638823178 27315 28656 29111 29694 30 285 387 410 4294 4467 5949 25386 2789834880 41169 42614 31 474 545 1320 10506 13186 18126 27110 31498 3535336193 37322 32 1075 1130 1424 11390 13312 14161 16927 25071 25844 3428738151 33 161 396 427 5944 17281 22201 25218 30143 35566 38261 42513 34233 247 694 1446 3180 3507 9069 20764 21940 33422 39358 35 271 508 10136271 21760 21858 24887 29808 31099 35475 39924 36 8 674 1329 3135 511014460 28108 28388 31043 31137 31863 37 1035 1222 1409 8287 16083 2445024888 29356 30329 37834 39684 38 391 1090 1128 1866 4095 10643 1312114499 20056 22195 30593 39 55 161 1402 6289 6837 8791 17937 21425 2660230461 37241 40 110 377 1228 6875 13253 17032 19008 23274 32285 3345241630 41 360 638 1355 5933 12593 13533 23377 23881 24586 26040 41663 42535 1240 1333 3354 10860 16032 32573 34908 34957 39255 40759 43 526 9361321 7992 10260 18527 28248 29356 32636 34666 35552 44 336 785 875 753013062 13075 18925 27963 28703 33688 36502 45 36 591 1062 1518 3821 704811197 17781 19408 22731 24783 46 214 1145 1223 1546 9475 11170 1606121273 38688 40051 42479 47 1136 1226 1423 20227 22573 24951 26462 2958634915 42441 43048 48 26 276 1425 6048 7224 7917 8747 27559 28515 3500237649 49 127 294 437 4029 8585 9647 11904 24115 28514 36893 39722 50 7481093 1403 9536 19305 20468 31049 38667 40502 40720 41949 51 96 638 7439806 12101 17751 22732 24937 32007 32594 38504 52 649 904 1079 2770 33379158 20125 24619 32921 33698 35173 53 401 518 984 7372 12438 12582 1870435874 39420 39503 39790 54 10 451 1077 8078 16320 17409 25807 2881430613 41261 42955 55 405 592 1178 15936 18418 19585 21966 24219 3063734536 37838 56 50 584 851 9720 11919 22544 22545 25851 35567 41587 4187657 911 1113 1176 1806 10058 10809 14220 19044 20748 29424 36671 58 441550 1135 1956 11254 18699 30249 33099 34587 35243 39952 59 510 1016 12818621 13467 13780 15170 16289 20925 26426 34479 60 4969 5223 17117 2195022144 24043 27151 39809 61 11452 13622 18918 19670 23995 32647 3720037399 62 6351 6426 13185 13973 16699 22524 31070 31916 63 4098 1061714854 18004 28580 36158 37500 38552

In another example, when the length N of the LDPC codeword is 16200 andthe code rate is 6/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 28 presented below:

TABLE 28 Indexes of rows where 1 is located in i the 0th column of theith column group 0 15 593 1066 1714 5358 6168 7077 7979 1 339 731 7691399 4678 7100 8114 8696 2 247 344 510 5273 5668 6136 8569 9147 3 21 283521 4055 4548 4957 6557 7718 4 3 110 880 1410 4143 8297 9105 9115 5 2559 636 1934 2947 3765 4060 5072 6 741 754 1040 1827 2112 3338 4693 64987 213 338 775 2464 2974 3852 4353 4787 8 211 428 432 2439 2694 4541 60258071 9 28 239 855 2060 3791 7217 8722 10 407 555 814 2635 3037 4619 847311 203 846 988 2599 4890 7749 9671 12 641 632 801 2577 4612 4916 5286 13111 577 728 2998 4109 5547 8002 14 197 391 480 1526 9016 9434 9447 15382 446 546 3865 6824 7752 8076 16 307 321 1031 4476 7858 8463 9604 17112 252 446 1665 2189 4869 5570 18 4566 6695 7966 8371 9608 19 2490 34196716 9038 9232 20 1117 1203 6031 7193 7320

In another example, when the length N of the LDPC codeword is 64800 andthe code rate is 6/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 29 presented below:

TABLE 29 Index of row where 1 is located in I the 0th column of the ithcolumn group 0 71 276 856 6867 12964 17373 18159 26420 28460 28477 1 257322 672 2533 5316 6578 9037 10231 13845 36497 2 233 765 904 1366 387513145 15409 18620 23910 30825 3 100 224 405 12776 13868 14787 1678123886 29099 31419 4 23 496 891 2512 12589 14074 19392 20339 27658 286845 473 712 759 1283 4374 9898 12551 13814 24242 32728 6 511 567 815 1182317106 17900 19338 22315 24396 26448 7 45 733 836 1923 3727 17468 2574633806 35995 36657 8 17 487 675 2670 3922 5145 18009 23993 31073 36624 972 751 773 1937 17324 28512 30666 30934 31016 31849 10 257 343 594 1404119141 24914 26864 28809 32055 34753 11 99 241 491 2650 9670 17433 1778518988 22235 30742 12 198 299 655 6737 8304 10917 16092 19387 20755 3769013 351 916 926 18151 21708 23216 30321 33578 34052 37949 14 54 332 3732010 3332 5623 16301 34337 36451 37861 15 139 257 1068 11090 20289 2969429732 32640 35133 36404 16 457 855 968 2155 4956 5422 5949 17570 2667332387 17 137 570 619 5006 6099 7979 14429 16650 25443 32789 18 46 282287 10258 18383 20258 27186 27494 28429 38266 19 445 486 1058 1868 997611294 20364 23695 30826 35330 20 134 900 931 12518 14544 17715 1962321111 33668 34570 21 65 66 586 8020 20270 23831 31041 31965 32224 3518922 174 290 784 6740 14673 17642 26286 27382 33447 34879 23 332 675 10331838 12004 15439 20765 31721 34225 38863 24 527 558 832 3867 6318 831710883 13466 18427 25377 25 431 780 1021 1112 2873 7675 13059 17793 2057020771 26 339 536 1015 5725 6916 10846 14487 21156 28123 32614 27 456 8301078 7511 11801 12362 12705 17401 28867 34032 28 222 538 989 5593 60228302 14008 23445 25127 29022 29 37 393 788 3025 7768 11367 22276 2276128232 30394 30 234 257 1045 1307 2908 6337 26530 28142 34129 35997 31 3546 978 9912 9978 12567 17843 24194 34887 35206 32 39 959 967 5027 1084714657 18859 28075 28214 36325 33 275 477 823 11376 18073 28997 3052131661 31941 32116 34 185 580 966 11733 12013 12760 13358 19372 3253435504 35 760 891 1046 11150 20358 21638 29930 31014 33050 64840 36 360389 1057 5316 5938 14186 16404 32445 34021 35722 37 306 344 679 52246674 10305 18753 25583 30585 36943 38 103 171 1016 8780 11741 1214419470 20955 22495 27377 39 818 832 894 3883 14279 14497 22505 2612928719 31246 40 215 411 760 5886 25612 28556 32213 32704 35901 36130 41229 489 1067 2385 8587 20565 23431 28102 30147 32859 42 288 664 980 81388531 21676 23787 26708 28798 34490 43 89 552 847 6656 9889 23949 2622627080 31236 35823 44 66 142 443 3339 3913 7977 14944 15464 19186 2598345 605 876 931 16682 17669 25800 28220 33432 35738 37382 46 346 423 8065669 7668 8789 9928 19724 24039 27893 47 48 460 1055 3512 7389 754920216 22180 28221 35437 48 187 636 824 1678 4508 13588 19683 21750 3031133480 49 25 768 935 2856 8187 9052 21850 29941 33217 34293 50 349 624716 2698 6395 6435 8974 10649 15932 17378 51 336 410 871 3582 9830 1088513892 18027 19203 36659 52 176 849 1078 17302 19379 27964 28164 2872032557 35495 53 234 890 1075 9431 9605 9700 10113 11332 12679 24268 54516 638 733 8851 19871 22740 25791 30152 32659 35568 55 253 830 879 208616885 22952 23765 25389 34656 37293 56 94 954 998 2003 3369 6870 732129856 31373 34888 57 79 350 933 4853 6252 11932 12058 21631 24552 2487658 246 647 778 4036 10391 10656 13194 32335 32360 34179 59 149 339 4366971 8356 8715 11577 22376 28684 31249 60 36 149 220 6936 18408 1919219288 23063 28411 35312 61 273 683 1042 6327 10011 18041 21704 2909730791 31425 62 46 138 722 2701 10964 13002 19930 26625 26456 28965 63 121009 1040 1990 2930 5302 21215 22625 23011 29288 64 125 241 819 22453199 8415 21133 26786 27226 38838 65 45 476 1075 7393 15141 20414 312443336 35004 38391 66 432 578 667 1343 10466 11314 11507 23314 27720 3446567 248 291 556 1971 3989 8992 18000 19998 23932 34652 68 68 694 837 22467472 7873 11078 12868 20937 35591 69 272 924 949 2030 4360 6203 973719705 19902 38039 70 21 314 979 2311 2632 4109 19527 21920 31413 3427771 197 253 804 1249 4315 10021 14358 20559 27099 30525 72 9802 1616417499 22378 22403 22704 26742 29908 73 9064 10904 12305 14057 1615626000 32613 34536 74 5178 6319 10239 19343 25628 30577 31110 32291

In another example, when the length N of the LDPC codeword is 16200 andthe code rate is 7/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 30 presented below:

TABLE 30 Indexes of rows where 1 is located i in the 0th column of theith column group 0 56 330 835 1133 1731 2171 5077 7762 1 21 259 845 18272503 3258 7361 7490 2 105 779 1069 1366 7074 7251 7294 7514 3 16 558 9232455 4076 6294 7507 8475 4 37 197 384 2184 2223 6347 6525 7258 5 197 393844 1961 3881 5842 6368 8032 6 374 588 1069 3093 4484 5868 7320 7 243767 790 1603 1867 4804 7416 8 0 242 730 2141 4235 4642 5063 9 148 327431 2291 3847 5133 7977 10 110 864 925 2730 4227 6604 7219 11 571 746867 1384 3974 5944 6713 12 268 347 948 1515 3629 5598 7538 13 876 9041049 4249 5198 6938 7701 14 690 748 782 1304 2117 4528 4589 15 14 300703 2968 4571 6102 7754 16 832 998 1071 2591 3865 4812 6321 17 458 903976 5179 5520 6862 8068 18 155 358 984 1417 1602 2697 3044 19 312 701784 1636 2183 3501 5170 20 85 981 989 2893 2951 4457 4685 21 5091 52445293 5404 6009 22 2171 2203 2344 3255 6338 23 3072 4338 6965 7045 8061

In another example, when the length N of the LDPC codeword is 64800 andthe code rate is 7/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 31 presented below:

TABLE 31 Indexes of rows where 1 is located i in the 0th column of theith column group 0 460 792 1007 4580 11452 13130 26882 27020 32439 1 35472 1056 7154 12700 13326 13414 16828 19102 2 45 440 772 4854 7863 2694527684 28651 31875 3 744 812 892 1509 9018 12925 14140 21357 25106 4 271474 761 4268 6706 9609 19701 19707 24870 5 223 477 662 1987 9247 1837622148 24948 27694 6 44 379 786 8823 12322 14666 16377 28688 29924 7 104219 562 5832 19665 20615 21043 22759 32180 8 41 43 870 7963 13718 1413617216 30470 33428 9 592 744 887 4513 6192 18116 19482 25032 34095 10 456821 1078 7162 7443 8774 15567 17243 33085 11 151 666 977 6946 1035811172 18129 19777 32234 12 236 793 870 2001 6805 9047 13877 30131 3425213 297 698 772 3449 4204 11608 22950 26071 27512 14 202 428 474 32053726 6223 7708 20214 25283 15 139 719 915 1447 2938 11864 15932 2174828598 16 135 853 902 3239 18590 20579 30578 33374 34045 17 9 13 97111834 13642 17628 21669 24741 30965 18 344 531 730 1880 16895 1758721901 28620 31957 19 7 192 380 3168 3729 5518 6827 20372 34168 20 28 521681 4313 7465 14209 21501 23364 25980 21 269 393 898 3561 11066 1198517311 26127 30309 22 42 82 707 4880 4890 9618 23340 25959 31695 23 189262 707 6573 14082 22259 24230 24390 24664 24 383 568 573 5498 1344913990 16904 22629 34203 25 585 596 820 2440 2488 21956 28261 28703 2959126 755 763 795 5636 16433 21714 23452 31150 34545 27 23 343 669 11593507 13096 17978 24241 34321 28 316 384 944 4872 8491 18913 21085 2319824798 29 64 314 765 3706 7136 8634 14227 17127 23437 30 220 693 899 879112417 13487 18335 22126 27428 31 285 794 1045 8624 8801 9547 19167 2189432657 32 386 621 1045 1634 1882 3172 13686 16027 22448 33 95 622 6932827 7098 11452 14112 18831 31308 34 446 813 928 7976 8935 13146 2711727766 33111 35 89 138 241 3218 9283 20458 31484 31538 34216 36 277 420704 9281 12576 12788 14496 15357 20585 37 141 643 758 4894 10264 1514416357 22478 26461 38 17 108 160 13183 15424 17939 19276 23714 26655 39109 285 608 1682 20223 21791 24615 29622 31983 40 123 515 622 7037 1394615292 15606 16262 23742 41 264 565 923 6460 13622 13934 23181 2547526134 42 202 548 789 8003 10993 12478 16051 25114 27579 43 121 450 5755972 10062 18693 21852 23874 28031 44 507 560 889 12064 13316 1962921547 25461 28732 45 664 786 1043 9137 9294 10163 23389 31436 34297 4645 830 907 10730 16541 21232 30354 30605 31847 47 203 507 1060 697112216 13321 17861 22671 29825 48 369 881 952 3035 12279 12775 1768217805 34281 49 683 709 1032 3787 17623 24138 26775 31432 33626 50 524792 1042 12249 14765 18601 25811 32422 33163 51 137 639 688 7182 816910443 22530 24597 29039 52 159 643 749 16386 17401 24135 28429 3346833469 53 107 481 555 7322 13234 19344 23498 26581 31378 54 249 389 5233421 10150 17616 19085 20545 32069 55 395 738 1045 2415 3005 3820 1954123543 31068 56 27 293 703 1717 3460 8326 8501 10290 32625 57 126 247 5156031 9549 10643 22067 29490 34450 58 331 471 1007 3020 3922 7580 2335828620 30946 59 222 542 1021 3291 3652 13130 16349 33009 34348 60 532 7191038 5891 7528 23252 25472 31395 31774 61 145 398 774 7816 13887 1493623708 31712 33160 62 88 536 600 1239 1887 12195 13782 16726 27998 63 151269 585 1445 3178 3970 15568 20358 21051 64 650 819 865 15567 1854625571 32038 33350 33620 65 93 469 800 6059 10405 12296 17515 21354 2223166 97 206 951 6161 16376 27022 29192 30190 30665 67 412 549 986 583310583 10766 24946 28878 31937 68 72 604 659 5267 12227 21714 32120 3347233974 69 25 902 912 1137 2975 9642 11598 25919 28278 70 420 976 10558473 11512 20198 21662 25443 30119 71 1 24 932 6426 11899 13217 1393516548 29737 72 53 618 988 6280 7267 11676 13575 15532 25787 73 111 739809 8133 12717 12741 20253 20608 27850 74 120 683 943 14496 15162 1544018660 27543 32404 75 600 754 1055 7873 9679 17351 27268 33508 76 344 7561054 7102 7193 22903 24720 27883 77 582 1003 1046 11344 23756 2749727977 32853 78 28 429 509 11106 11767 12729 13100 31792 79 131 555 9075113 10259 10300 20580 23029 80 406 915 977 12244 20259 26616 2789932228 81 46 195 224 1229 4116 10263 13608 17830 82 19 819 953 7965 999813959 30580 30754 83 164 1003 1032 12920 15975 16582 22624 27357 84 843311894 13531 17675 25889 31384 85 3166 3813 8596 10368 25104 29584 862466 8241 12424 13376 24837 32711

Hereinafter, positions of rows where 1 exists in the matrix A and thematrix C will be explained with reference to Table 24 by way of anexample.

Since the length N of the LDPC codeword is 16200 and the code rate is4/15 in Table 24, M₁=1080, M₂=10800, Q₁=3, and Q₂=30 in the parity checkmatrix 400 defined by Table 24 with reference to Table 22.

Herein, Q₁ is a size by which columns of the same column group arecyclic-shifted in the matrix A, and Q₂ is a size by which columns of thesame column group are cyclic-shifted in the matrix C.

In addition, Q₁=M₁/L, Q₂=M₂/L, M₁=g, and M₂=N−K−g, and L is an intervalat which a pattern of a column is repeated in the matrix A and thematrix C, and for example, may be 360.

The index of the row where 1 is located in the matrix A and the matrix Cmay be determined based on the M₁ value.

For example, since M₁=1080 in the case of Table 24, the positions of therows where 1 exists in the 0^(th) column of the ith column group in thematrix A may be determined based on values smaller than 1080 from amongthe index values of Table 24, and the positions of the rows where 1exists in the 0^(th) column of the ith column group in the matrix C maybe determined based on values greater than or equal to 1080 from amongthe index values of Table 24.

Specifically, in Table 24, the sequence corresponding to the 0^(th)column group is “19, 585, 710, 3241, 3276, 3648, 6345, 9224, 9890, and10841”. Accordingly, in the case of the 0^(th) column of the 0^(th)column group of the matrix A, 1 may be located in the 19^(th) row,585^(th) row, and 710^(th) row, and, in the case of the 0^(th) column ofthe 0^(th) column group of the matrix C, 1 may be located in the3241^(st) row, 3276^(th) row, 3648^(th) row, 6345^(th) row, 9224^(th)row, 9890^(th) row, and 10841^(st) row.

Once positions of 1 in the 0^(th) column of each column group of thematrix A are defined, positions of rows where 1 exists in another columnof each column group may be defined by cyclic-shifting from the previouscolumn by Q₁. Once positions of 1 in the 0^(th) column of each columngroup of the matrix C are defined, position of rows where 1 exists inanother column of each column group may be defined by cyclic-shiftingfrom the previous column by Q₂.

In the above-described example, in the case of the 0^(th) column of the0^(th) column group of the matrix A, 1 exists in the 19^(th) row,585^(th) row, and 710^(th) row. In this case, since Q₁=3, the indexes ofrows where 1 exists in the 1^(st) column of the 0^(th) column group are22(=19+3), 588(=585+3), and 713(=710+3), and the index of rows where 1exists in the 2^(nd) column of the 0^(th) column group are 25(=22+3),591 (=588+3), and 716(=713+3).

In the case of the 0^(th) column of the 0^(th) column group of thematrix C, 1 exists in the 3241^(st) row, 3276^(th) row, 3648^(th) row,6345^(th) row, 9224^(th) row, 9890^(th) row, and 10841^(st) row. In thiscase, since Q₂=30, the index of rows where 1 exists in the 1^(st) columnof the 0^(th) column group are 3271 (=3241+30), 3306(=3276+30), 3678(=3648+30), 6375 (=6345+30), 9254 (=9224+30), 9920 (=9890+30), and 10871(=10841+30), and the indexes of rows where 1 exists in the 2^(nd) columnof the 0^(th) column group are 3301 (=3271+30), 3336(=3306+30), 3708(=3678+30), 6405 (=6375+30), 9284 (=9254+30), 9950 (=9920+30), 10901(=10871+30).

In this method, the positions of rows where 1 exists in all columngroups of the matrix A and the matrix C are defined.

The matrix B may have a dual diagonal configuration, the matrix D mayhave a diagonal configuration (that is, the matrix D is an identitymatrix), and the matrix Z may be a zero matrix.

As a result, the parity check matrix 400 shown in FIG. 4 may be definedby the matrices A, B, C, D, and Z having the above-describedconfigurations.

Hereinafter, a method for performing LDPC encoding based on the paritycheck matrix 400 shown in FIG. 4 will be explained. An LDPC encodingprocess when the parity check matrix 400 is defined as shown in Table 24by way of an example will be explained for the convenience ofexplanation.

For example, when an information word block S=(s₀, s₁, S_(K−1)) isLDPC-encoded, an LDPC codeword Λ=(λ₀, λ₁, . . . λ_(N-1))=(s₀, s₁, . . .S_(K−1), p₀, p₁, . . . , P_(M) ₁ _(+M) ₂ ₋₁) including a parity bitP=(p₀, p₁, . . . , P_(M) ₁ _(+M) ₂ ₋₁).

M₁ and M₂ indicate the size of the matrix B having the dual diagonalconfiguration and the size of the matrix C having the diagonalconfiguration, respectively, and M₁=g, M₂=N−K−g.

A process of calculating a parity bit is as follows. In the followingexplanation, the parity check matrix 400 is defined as shown in Table 24by way of an example, for the convenience of explanation.

Step 1) λ and p are initialized as λ_(i)=s₁ (i=0, 1, . . . , K−1),p_(j)=0 (j=0, 1, . . . , M₁+M₂−1).

Step 2) The 0^(th) information word bit λ₀ is accumulated in the addressof the parity bit defined in the first row (that is, the row of i=0) ofTable 24. This may be expressed by Equation 12 presented below:

$\begin{matrix}{{P_{19} = {P_{19} \oplus \lambda_{0}}}{P_{585} = {P_{585} \oplus \lambda_{0}}}{P_{710} = {P_{710} \oplus \lambda_{0}}}{P_{3241} = {P_{3241} \oplus \lambda_{0}}}{P_{3276} = {P_{3276} \oplus \lambda_{0}}}{P_{3648} = {P_{3648} \oplus \lambda_{0}}}{P_{6345} = {P_{6345} \oplus \lambda_{0}}}{P_{9224} = {P_{9224} \oplus \lambda_{0}}}{P_{9890} = {P_{9890} \oplus \lambda_{0}}}{P_{10841} = {P_{10841} \oplus \lambda_{0}}}} & (12)\end{matrix}$

Step 3) Regarding the next L−1 number of information word bits λ_(m)(m=1, 2, . . . , L−1), λ_(m) is accumulated in the parity bit addresscalculated based on Equation 13 presented below:

(χ+m×Q ₁)mod M ₁ (if χ<M ₁)

M ₁+{(χM ₁ +m×Q ₂)mod M ₂} (if χ≥M ₁)  (13)

Herein, x is an address of a parity bit accumulator corresponding to the0^(th) information word bit λ₀.

In addition, Q₁=M₁/L and Q₂=M₂/L. In addition, since the length N of theLDPC codeword is 16200 and the code rate is 4/15 in Table 24, M₁=1080,M₂=10080, Q₁=3, Q₂=30, and L=360 with reference to Table 22.

Accordingly, an operation as shown in Equation 14 presented below may beperformed for the 1^(st) information word bit λ₁:

$\begin{matrix}{{P_{22} = {P_{22} \oplus \lambda_{1}}}{P_{588} = {P_{588} \oplus \lambda_{1}}}{P_{713} = {P_{713} \oplus \lambda_{1}}}{P_{3271} = {P_{3271} \oplus \lambda_{1}}}{P_{3306} = {P_{3306} \oplus \lambda_{1}}}{P_{3678} = {P_{3678} \oplus \lambda_{1}}}{P_{6375} = {P_{6375} \oplus \lambda_{1}}}{P_{9254} = {P_{9254} \oplus \lambda_{1}}}{P_{9920} = {P_{9920} \oplus \lambda_{1}}}{P_{10871} = {P_{10871} \oplus \lambda_{1}}}} & (14)\end{matrix}$

Step 4) Since the same address of the parity bit as in the second row(that is the row of i=1) of Table 24 is given to the Lth informationword bit λ_(L), in a similar method to the above-described method, theaddress of the parity bit regarding the next L−1 number of informationword bits λ_(m) (m=L+1, L+2, . . . , 2L−1) is calculated based onEquation 13. In this case, x is the address of the parity bitaccumulator corresponding to the information word bit 4, and may beobtained based on the second row of Table 24.

Step 5) The above-described processes are repeated for L number of newinformation word bits of each group by considering new rows of Table 24as the address of the parity bit accumulator.

Step 6) After the above-described processes are repeated for thecodeword bits λ₀ to λ_(K−1), values regarding Equation 15 presentedbelow are calculated in sequence from i=1:

P _(i) =P _(i) ⊕P _(i-1)(i=1,2, . . . ,M ₁−1)  (15)

Step 7) Parity bits λ_(K) to λ_(K+M) ₁ ₋₁ corresponding to the matrix Bhaving the dual diagonal configuration are calculated based on Equation16 presented below:

λ_(K+L×t+s) =p _(Q) ₁ _(×S+t)(0≤s<L,0≤t<Q ₁)  (16)

Step 8) The address of the parity bit accumulator regarding L number ofnew codeword bits λ_(K) to λ_(K+M) ₁ ₋₁ of each group is calculatedbased on Table 24 and Equation 13.

Step 9) After the codeword bits λ_(K) to λ_(K+M) ₁ ₋₁ are calculated,parity bits λ_(K+M) ₁ to λ_(K+M) ₁ _(+M) ₂ ₋₁ corresponding to thematrix C having the diagonal configuration are calculated based onEquation 17 presented below:

λ_(K+M) ₁ _(+L×t+s) =p _(M) ₁ _(+Q) ₂ _(×S+t)(0≤s<L,0≤t<Q ₂)  (17)

As a result, the parity bits may be calculated in the above-describedmethod.

Referring back to FIG. 1, the encoder 110 may perform the LDPC encodingby using various code rates such as 3/15, 4/15, 5/15, 6/15, 7/15, 8/15,9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, the encoder 110 maygenerate an LDPC codeword having various lengths such as 16200, 64800,etc., based on the length of the information word bits and the coderate.

In this case, the encoder 110 may perform the LDPC encoding by using theparity check matrix, and the parity check matrix is configured as shownin FIGS. 2 to 4.

In addition, the encoder 110 may perform Bose, Chaudhuri, Hocquenghem(BCH) encoding as well as LDPC encoding. To achieve this, the encoder110 may further include a BCH encoder (not shown) to perform BCHencoding.

In this case, the encoder 110 may perform encoding in an order of BCHencoding and LDPC encoding. Specifically, the encoder 110 may add BCHparity bits to input bits by performing BCH encoding and LDPC-encodesthe information word bits including the input bits and the BCH paritybits, thereby generating the LDPC codeword.

The interleaver 120 interleaves the LDPC codeword. That is, theinterleaver 120 receives the LDPC codeword from the encoder 110, andinterleaves the LDPC codeword based on various interleaving rules.

In particular, the interleaver 120 may interleave the LDPC codeword suchthat a bit included in a predetermined bit group from among a pluralityof bit groups constituting the LDPC codeword (that is, a plurality ofgroups or a plurality of blocks) is mapped onto a predetermined bit of amodulation symbol.

In this case, the interleaver 120 may interleave the LDPC codeword suchthat bits included in continuous bit groups from among the plurality ofbit groups of the LDPC codeword are mapped onto the same modulationsymbol.

In addition, when check nodes connected only to a single parity bit inthe parity check matrix of the LDPC code exists in plurality number, theinterleaver 120 may interleave the LDPC codeword such that bits includedin the bit groups corresponding to the parity bit to which the checknodes are connected are selectively mapped onto the modulation symbol.

Accordingly, the modulator 130 may map the bit included in thepredetermined bit group from among the plurality of bit groups of theLDPC codeword onto a predetermined bit of the modulation symbol.

That is, the modulator 130 may map the bits included in the continuousbit groups from among the plurality of bit groups of the LDPC codewordonto the same modulation symbol. In addition, when the check nodesconnected only to a single parity bit in the parity check matrix of theLDPC code exists in plurality number, the modulator 130 may selectivelymap the bits included in the bit groups corresponding to the parity bitto which the check nodes are connected onto the same modulation symbol.

To achieve this, as shown in FIG. 5, the interleaver 120 may include aparity interleaver 121, a group interleaver (or a group-wise interleaver122), a group twist interleaver 123 and a block interleaver 124.

The parity interleaver 121 interleaves the parity bits constituting theLDPC codeword.

Specifically, when the LDPC codeword is generated based on the paritycheck matrix 200 having the configuration of FIG. 2, the parityinterleaver 121 may interleave only the parity bits of the LDPC codewordby using Equations 18 presented below:

u _(i) =c _(i) for 0≤i<K _(ldpc), and

u _(K) _(ldpc) _(+M·t+s) =c _(K) _(ldpc) _(+Q) _(ldpc) _(·s+t) for0≤s<M,0≤t<Q _(ldpc)  (18),

where M is an interval at which a pattern of a column group is repeatedin the information word submatrix 210, that is, the number of columnsincluded in a column group (for example, M=360), and Q_(ldpc) is a sizeby which each column is cyclic-shifted in the information word submatrix210. That is, the parity interleaver 121 performs parity interleavingwith respect to the LDPC codeword c=(c₀, c₁, . . . , c_(N) _(ldpc) ₋₁),and outputs U=(u₀, u₁, . . . , u_(N) _(ldpc) ₋₁).

The LDPC codeword parity-interleaved in the above-described method maybe configured such that a predetermined number of continuous bits of theLDPC codeword have similar decoding characteristics (cycle distribution,a degree of a column, etc.).

For example, the LDPC codeword may have the same characteristics on thebasis of M number of continuous bits. Herein, M is an interval at whicha pattern of a column group is repeated in the information wordsubmatrix 210 and, for example, may be 360.

Specifically, a product of the LDPC codeword bits and the parity checkmatrix should be “0”. This means that a sum of products of the i^(th)LDPC codeword bit, c₁(i=0, 1, . . . , N_(ldpc)−1) and the i^(th) columnof the parity check matrix should be a “0” vector. Accordingly, thei^(th) LDPC codeword bit may be regarded as corresponding to the i^(th)column of the parity check matrix.

In the case of the parity check matrix 200 of FIG. 2, M number ofcolumns in the information word submatrix 210 belong to the same groupand the information word submatrix 210 has the same characteristics onthe basis of a column group (for example, the columns belonging to thesame column group have the same degree distribution and the same cyclecharacteristic).

In this case, since M number of continuous bits in the information wordbits correspond to the same column group of the information wordsubmatrix 210, the information word bits may be formed of M number ofcontinuous bits having the same codeword characteristics. When theparity bits of the LDPC codeword are interleaved by the parityinterleaver 121, the parity bits of the LDPC codeword may be formed of Mnumber of continuous bits having the same codeword characteristics.

However, regarding the LDPC codeword encoded based on the parity checkmatrix 300 of FIG. 3 and the parity check matrix 400 of FIG. 4, parityinterleaving may not be performed. In this case, the parity interleaver121 may be omitted.

The group interleaver 122 may divide the parity-interleaved LDPCcodeword into a plurality of bit groups and rearrange the order of theplurality of bit groups in bit group wise (or bit group unit). That is,the group interleaver 122 may interleave the plurality of bit groups inbit group wise.

According to an exemplary embodiment, when the parity interleaver 121 isomitted, the group interleaver 122 may divide the LDPC codeword into aplurality of bit groups and rearrange the order of the plurality of bitgroups in bit group wise.

To achieve this, the group interleaver 122 divides theparity-interleaved LDPC codeword into a plurality of bit groups by usingEquation 19 or Equation 20 presented below.

$\begin{matrix}{\mspace{79mu} {X_{j} = {{\left\{ {{\left. u_{k} \middle| j \right. = \left\lfloor \frac{k}{360} \right\rfloor},{0 \leq k < N_{ldpc}}} \right\} \mspace{14mu} {for}\mspace{14mu} 0} \leq j < N_{group}}}} & (19) \\{{X_{j} = {{\left\{ {\left. u_{k} \middle| {{360 \times j} \leq k < {360 \times \left( {j + 1} \right)}} \right.,{0 \leq k < N_{ldpc}}} \right\} \mspace{14mu} {for}\mspace{14mu} 0} \leq j < N_{group}}},} & (20)\end{matrix}$

where N_(group) is the total number of bit groups, X_(j) is the j^(th)bit group, and u_(k) is the k^(th) LDPC codeword bit input to the groupinterleaver 122. In addition,

$\left\lfloor \frac{k}{360} \right\rfloor$

is the largest integer below k/360.

Since 360 in these equations indicates an example of the interval M atwhich the pattern of a column group is repeated in the information wordsubmatrix, 360 in these equations can be changed to M.

The LDPC codeword which is divided into the plurality of bit groups maybe as shown in FIG. 6.

Referring to FIG. 6, the LDPC codeword is divided into the plurality ofbit groups and each bit group is formed of M number of continuous bits.When M is 360, each of the plurality of bit groups may be formed of 360bits. Accordingly, the bit groups may be formed of bits corresponding tothe column groups of the parity check matrix.

Specifically, since the LDPC codeword is divided by M number ofcontinuous bits, K_(ldpc) number of information word bits are dividedinto (K_(ldpc)/M) number of bit groups and N_(ldpc)−K_(ldpc) number ofparity bits are divided into (N_(ldpc)−K_(ldpc))/M number of bit groups.Accordingly, the LDPC codeword may be divided into (N_(ldpc)/M) numberof bit groups in total.

For example, when M=360 and the length N_(ldpc) of the LDPC codeword is64800, the number of bit groups N_(groups) is 180(=64800/360), and, whenthe M=360 and the length N_(ldpc) of the LDPC codeword is 16200, thenumber of bit groups N_(group) is 45(=16200/360).

As described above, the group interleaver 122 divides the LDPC codewordsuch that M number of continuous bits are included in a same group sincethe LDPC codeword has the same codeword characteristics on the basis ofM number of continuous bits. Accordingly, when the LDPC codeword isgrouped by M number of continuous bits, the bits having the samecodeword characteristics belong to the same group.

In the above-described example, the number of bits constituting each bitgroup is M. However, this is merely an example and the number of bitsconstituting each bit group is variable.

For example, the number of bits constituting each bit group may be analiquot part of M. That is, the number of bits constituting each bitgroup may be an aliquot part of the number of columns constituting acolumn group of the information word submatrix of the parity checkmatrix. In this case, each bit group may be formed of aliquot part of Mnumber of bits. For example, when the number of columns constituting acolumn group of the information word submatrix is 360, that is, M=360,the group interleaver 122 may divide the LDPC codeword into a pluralityof bit groups such that the number of bits constituting each bit groupis one of the aliquot parts of 360.

In the following explanation, the number of bits constituting a bitgroup is M by way of an example, for the convenience of explanation.

Thereafter, the group interleaver 122 interleaves the LDPC codeword inbit group wise. Specifically, the group interleaver 122 may group theLDPC codeword into the plurality of bit groups and rearrange theplurality of bit groups in bit group wise. That is, the groupinterleaver 122 changes positions of the plurality of bit groupsconstituting the LDPC codeword and rearranges the order of the pluralityof bit groups constituting the LDPC codeword in bit group wise.

Herein, the group interleaver 122 may rearrange the order of theplurality of bit groups in bit group wise such that bit groups includingbits mapped onto the same modulation symbol from among the plurality ofbit groups are spaced apart from one another at predetermined intervals.

In this case, the group interleaver 122 may rearrange the order of theplurality of bit groups in bit group wise by considering at least one ofthe number of rows and columns of the block interleaver 124, the numberof bit groups of the LDPC codeword, and the number of bits included ineach bit group, such that bit groups including bits mapped onto the samemodulation symbol are spaced apart from one another at predeterminedintervals.

To achieve this, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bit group wise by using Equation 21presented below:

Y _(j) =X _(π(j))(0≤j<N _(group))  (21),

where X_(j) is the j^(th) bit group before group interleaving, and Y_(j)is the j^(th) bit group after group interleaving. In addition, π(j) is aparameter indicating an interleaving order and is determined by at leastone of a length of an LDPC codeword, a modulation method, and a coderate. That is, π(j) denotes a permutation order for group wiseinterleaving.

Accordingly, X_(π(j)) is a π(j)^(th) bit group before groupinterleaving, and Equation 21 means that the pre-interleaving π(j)^(th)bit group is interleaved into the j^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be definedas in Tables 32 to 56 presented below.

In this case, π(j) is defined according to a length of an LPDC codewordand a code rate, and a parity check matrix is also defined according toa length of an LDPC codeword and a code rate. Accordingly, when LDPCencoding is performed based on a specific parity check matrix accordingto a length of an LDPC codeword and a code rate, the LDPC codeword maybe interleaved in bit group wise based on π(j) satisfying thecorresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rateof 7/15 to generate an LDPC codeword of a length of 16200, the groupinterleaver 122 may perform interleaving by using π(j) which is definedaccording to the length of the LDPC codeword of 16200 and the code rateof 7/15 in Tables 32 to 56 presented below.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, thecode rate is 5/15, and the modulation method (or modulation format) isQuadrature Phase Shift Keying (QPSK), π(j) may be defined as in Table 32presented below. In particular, Table 32 may be applied when LDPCencoding is performed based on the parity check matrix defined by Table26.

TABLE 32 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 35 7 29 11 14 32 38 28 20 17 2539 19 4 1 12 10 30 0 44 43 2 21 Group-wise 5 13 34 37 23 15 36 18 42 1633 31 27 22 3 6 40 24 41 9 26 8 interleaver input

In the case of Table 32, Equation 21 may be expressed asY₀=X_(π(0))=X₃₅, Y₁=X_(π(1))=X₇, Y₂=X_(π(2))=X₂₉, . . . ,Y₄₃=X_(π(43))=X₂₆, and Y₄₄=X_(π(44))=X₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 35^(th) bit group to the 0^(th) bitgroup, the 7^(th) bit group to the 1^(st) bit group, the 29^(th) bitgroup to the 2^(nd) bit group, . . . , the 26^(th) bit group to the43^(rd) bit group, and the 8^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and the modulation method is QPSK, π(j)may be defined as in Table 33 presented below. In particular, Table 33may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 6.

TABLE 33 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 4 22 23 44 34 1 3 2 32 42 6 1530 40 18 5 28 38 7 14 26 36 9 Group-wise 0 16 43 33 17 11 12 31 41 21 2029 39 10 24 27 37 13 19 25 35 8 interleaver input

In the case of Table 33, Equation 21 may be expressed as Y₀=X_(π(0))=X₄,Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, andY₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group tothe 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . .. , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and the modulation method is QPSK, π(j)may be defined as in Table 34 presented below. In particular, Table 34may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 8.

TABLE 34 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 28 16 13 42 32 22 14 20 36 26 64 40 30 8 9 44 34 24 10 17 38 27 Group-wise 12 19 41 31 21 1 15 35 25 20 39 29 3 5 43 33 23 7 11 37 18 interleaver input

In the case of Table 34, Equation 21 may be expressed asY₀=X_(π(0))=X₂₈, Y₁=X_(π(1))=X₁₆, Y₂=X_(π(2))=X₁₃, . . . ,Y₄₃=X_(π(43))=X₃₇, and Y₄₄=X_(π(44))=X₁₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 28^(th) bit group to the 0^(th) bitgroup, the 16^(th) bit group to the 1^(st) bit group, the 13^(th) bitgroup to the 2^(nd) bit group, . . . , the 37^(th) bit group to the43^(rd) bit group, and the 18^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 11/15, and the modulation method is QPSK, π(j)may be defined as in Table 35 presented below. In particular, Table 35may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 10.

TABLE 35 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 1 2 40 14 27 24 36 7 9 11 12 4218 17 28 38 31 5 32 34 44 23 0 Group-wise 25 39 26 10 29 35 8 15 16 1341 3 6 4 37 19 22 20 33 43 30 21 interleaver input

In the case of Table 35, Equation 21 may be expressed as Y₀=X_(π(0))=X₁,Y₁=X_(π(1))=X₂, Y₂=X_(π(2))=X₄₀, . . . , Y₄₃=X_(π(43))=X₃₀, andY₄₄=X_(π(44))=X₂₁. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 1^(st) bit group to the 0^(th) bit group, the 2^(nd) bit group tothe 1^(st) bit group, the 40^(th) bit group to the 2^(nd) bit group, . .. , the 30^(th) bit group to the 43^(rd) bit group, and the 21^(st) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 13/15, and the modulation method is QPSK, π(j)may be defined as in Table 36 presented below. In particular, Table 36may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 12.

TABLE 36 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 26 10 12 38 28 15 0 44 34 24 148 40 30 20 13 42 32 22 11 9 36 25 Group-wise 7 5 37 27 4 16 43 33 23 218 39 29 19 6 41 31 21 3 17 35 1 interleaver input

In the case of Table 36, Equation 21 may be expressed asY₀=X_(π(0))=X₂₆, Y₁=X_(π(1))=X₁₀, Y₂=X_(π(2))=X₁₂, . . . ,Y₄₃=X_(π(43))=X₃₅, and Y₄₄=X_(π(44))=X₁. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 26^(th) bit group to the 0^(th) bitgroup, the 10^(th) bit group to the 1^(st) bit group, the 12^(th) bitgroup to the 2^(nd) bit group, . . . , the 35^(th) bit group to the43^(rd) bit group, and the 1^(st) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 5/15, and the modulation method is QPSK, π(j)may be defined as in Table 37 presented below. In particular, Table 37may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 4.

TABLE 37 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 5 20 30 40 12 18 28 38 1 7 2434 44 2 22 32 42 10 8 26 36 14 13 Group-wise 19 29 39 9 17 27 37 15 3 2333 43 16 21 31 41 0 4 25 35 11 6 interleaver input

In the case of Table 37, Equation 21 may be expressed as Y₀=X_(π(0))=X₅,Y₁=X_(π(1))=X₂₀, Y₂=X_(π(2))=X₃₀, . . . , Y₄₃=X_(π(43))=X₁₁, andY₄₄=X_(π(44))=X₆. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 5^(th) bit group to the 0^(th) bit group, the 20^(th) bit group tothe 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . .. , the 11^(th) bit group to the 43^(rd) bit group, and the 6^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and the modulation method is QPSK, π(j)may be defined as in Table 38 presented below. In particular, Table 38may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 5.

TABLE 38 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 26 10 12 38 28 15 0 44 34 24 148 40 30 20 13 42 32 22 11 9 36 25 Group-wise 7 5 37 27 4 16 43 33 23 218 39 29 19 6 41 31 21 3 17 35 1 interleaver input

In the case of Table 38, Equation 21 may be expressed asY₀=X_(π(0))=X₂₆, Y₁=X_(π(1))=X₁₀, Y₂=X_(π(2))=X₁₂, . . . ,Y₄₃=X_(π(43))=X₃₅, and Y₄₄=X_(π(44))=X₁. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 26^(th) bit group to the 0^(th) bitgroup, the 10^(th) bit group to the 1^(st) bit group, the 12^(th) bitgroup to the 2^(nd) bit group, . . . , the 35^(th) bit group to the43^(rd) bit group, and the 1^(st) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and the modulation method is QPSK, π(j)may be defined as in Table 39 presented below. In particular, Table 39may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 7.

TABLE 39 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 4 22 23 44 34 1 3 2 32 42 6 1530 40 18 5 28 38 7 14 26 36 9 Group-wise 0 16 43 33 17 11 12 31 41 21 2029 39 10 24 27 37 13 19 25 35 8 interleaver input

In the case of Table 39, Equation 21 may be expressed as Y₀=X_(π(0))=X₄,Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, andY₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group tothe 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . .. , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 11/15, and the modulation method is QPSK, π(j)may be defined as in Table 40 presented below. In particular, Table 40may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 9.

TABLE 40 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 4 22 23 44 34 1 3 2 32 42 6 1530 40 18 5 28 38 7 14 26 36 9 Group-wise 0 16 43 33 17 11 12 31 41 21 2029 39 10 24 27 37 13 19 25 35 8 interleaver input

In the case of Table 40, Equation 21 may be expressed as Y₀=X_(π(0))=X₄,Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, andY₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group tothe 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . .. , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 13/15, and the modulation method is QPSK, π(j)may be defined as in Table 41 presented below. In particular, Table 41may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 11.

TABLE 41 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 6 3 30 40 9 11 28 38 22 7 24 3444 13 8 32 42 1 12 26 36 0 10 Group-wise 15 29 39 17 19 27 37 2 4 23 3343 20 21 31 41 14 18 25 35 16 5 interleaver input

In the case of Table 41, Equation 21 may be expressed as Y₀=X_(π(0))=X₆,Y₁=X_(π(1))=X₃, Y₂=X_(π(2))=X₃₀, . . . , Y₄₃=X_(π(43))=X₁₆, andY₄₄=X_(π(44))=X₅. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 6^(th) bit group to the 0^(th) bit group, the 3^(rd) bit group tothe 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . .. , the 16^(th) bit group to the 43^(rd) bit group, and the 5^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and the modulation method is QPSK, π(j)may be defined as in Table 42 presented below. In particular, Table 42may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 6.

TABLE 42 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 3 22 7 18 6 1 4 14 5 15 2 23 2628 30 32 34 36 10 38 21 44 9 Group-wise 0 33 40 42 17 11 19 24 20 12 1625 27 29 31 13 35 37 39 41 43 8 interleaver input

In the case of Table 42, Equation 21 may be expressed as Y₀=X_(π(0))=X₃,Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₇, . . . , Y₄₃=X_(π(43))=X₄₃, andY₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 3^(rd) bit group to the 0^(th) bit group, the 22^(nd) bit group tothe 1^(st) bit group, the 7^(th) bit group to the 2^(nd) bit group, . .. , the 43^(rd) bit group to the 43^(rd) bit group, and the 8^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 5/15, and the modulation method is QPSK, π(j)may be defined as in Table 43 presented below.

TABLE 43 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 28 20 8 39 21 25 22 17 29 38 157 43 24 11 35 30 27 14 10 6 9 13 Group-wise 42 40 23 36 31 3 34 1 41 218 44 19 0 37 26 12 32 4 33 16 5 interleaver input

In the case of Table 43, Equation 21 may be expressed asY₀=X_(π(0))=X₂₈, Y₁=X_(π(1))=X₂₀, Y₂=X_(π(2))=X₈, . . . ,Y₄₃=X_(π(43))=X₁₆, and Y₄₄=X_(π(44))=X₅. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 28^(th) bit group to the 0^(th) bitgroup, the 20^(th) bit group to the 1^(st) bit group, the 8^(th) bitgroup to the 2^(nd) bit group, . . . , the 16^(th) bit group to the43^(rd) bit group, and the 5^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 44 presented below.

TABLE 44 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 36 2 31 18 13 6 40 43 29 26 2241 12 25 34 35 30 3 20 27 44 37 39 Group-wise 1 33 24 28 5 42 17 21 15 938 32 10 23 7 0 11 19 14 8 4 16 interleaver input

In the case of Table 44, Equation 21 may be expressed asY₀=X_(π(0))=X₃₆, Y₁=X_(π(1))=X₂, Y₂=X_(π(2))=X₃₁, . . . ,Y₄₃=X_(π(43))=X₄, and Y₄₄=X_(π(44))=X₁₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 36^(th) bit group to the 0^(th) bitgroup, the 2^(nd) bit group to the 1^(st) bit group, the 31^(st) bitgroup to the 2^(nd) bit group, . . . , the 4^(th) bit group to the43^(rd) bit group, and the 16^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and the modulation method is QPSK, π(j)may be defined as in Table 45 presented below.

TABLE 45 Order of bits group to be block interleaved j-th block π(j) (0≤ j < 45) of Group-wise 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 20 21 interleaver output 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 22 π(j)-th block of 12 39 21 17 11 0 24 26 16 40 225 36 20 41 32 33 19 44 7 15 23 30 Group-wise 43 9 14 4 8 25 6 35 37 1329 10 1 18 28 38 42 31 3 27 34 2 interleaver input

In the case of Table 45, Equation 21 may be expressed asY₀=X_(π(0))=X₁₂, Y₁=X_(π(1))=X₃₉, Y₂=X_(π(2))=X₂₁, . . . ,Y₄₃=X_(π(43))=X₃₄, and Y₄₄=X_(π(44))=X₂. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 12^(th) bit group to the 0^(th) bitgroup, the 39^(th) bit group to the 1^(st) bit group, the 21^(st) bitgroup to the 2^(nd) bit group, . . . , the 34^(th) bit group to the43^(rd) bit group, and the 2^(nd) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and the modulation method is QPSK, π(j)may be defined as in Table 46 presented below.

TABLE 46 Order of bits group to be block interleaved π(j) (0 ≤ j < 45)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block of 41 37 26 22 32 9 23 21 8 4 2515 10 17 19 16 2 6 36 3 30 24 1 Group-wise 29 13 5 0 34 27 42 12 33 4328 35 40 14 44 11 18 7 31 20 39 38 interleaver input

In the case of Table 46, Equation 21 may be expressed asY₀=X_(π(0))=X₄₁, Y₁=X_(π(1))=X₃₇, Y₂=X_(π(2))=X₂₆, . . . ,Y₄₃=X_(π(43))=X₃₉, and Y₄₄=X_(π(44))=X₃₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 41^(st) bit group to the 0^(th) bitgroup, the 37^(th) bit group to the 1^(st) bit group, the 26^(th) bitgroup to the 2^(nd) bit group, . . . , the 39^(th) bit group to the43^(rd) bit group, and the 38^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 5/15, and the modulation method is QPSK, π(j)may be defined as in Table 47 presented below.

TABLE 47 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 120 75 171 13 147 56 97 134 41 87 150 23 109 2 17877 62 148 130 50 96 34 18 Group wise 115 4 159 81 169 71 136 149 94 3921 110 121 60 8 174 73 131 142 157 40 24 107 interleaver 86 117 3 54 68175 140 154 164 16 28 100 82 42 119 65 179 143 132 5 17 162 104 input 9252 76 118 176 27 66 38 151 1 138 103 91 128 116 51 26 170 11 36 67 14579 98 127 112 155 48 25 173 15 64 137 37 84 126 95 153 74 105 163 7 5847 31 141 129 89 19 152 72 106 165 59 6 46 33 133 85 177 146 122 22 69167 0 111 55 99 45 12 32 83 125 139 158 70 168 57 113 102 44 30 88 12320 9 78 166 61 144 101 49 456 35 124 114 10 90 172 63 135 80 53 150 2943 108 14 93 161

In the case of Table 47, Equation 21 may be expressed asY₀=X_(π(0))=X₁₂₀, Y₁=X_(π(1))=X₇₅, Y₂=X_(π(2))=X₁₇₁, . . . ,Y₁₇₈=X_(π(178))=X₉₃, and Y_(π(179))=X_(π(179))=X₁₆₁. Accordingly, thegroup interleaver 122 may rearrange the order of the plurality of bitgroups in bit group wise by changing the 120^(th) bit group to the0^(th) bit group, the 75^(th) bit group to the 1^(st) bit group, the171^(st) bit group to the 2^(nd) bit group, . . . , the 93^(rd) bitgroup to the 178^(th) bit group, and the 161^(st) bit group to the179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 48 presented below.

TABLE 48 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 92 79 168 44 15 63 147 109 157 26 136 94 124 2 4214 64 176 105 155 92 144 86 Group-wise 116 133 24 38 65 9 167 102 156 55177 112 128 28 76 45 142 4 89 99 60 175 153 interleaver 118 35 19 129 46139 6 81 70 179 151 95 57 18 115 30 169 41 135 78 125 148 104 input 6216 91 29 161 40 3 174 51 73 123 113 61 84 97 13 34 138 172 158 0 23 7147 59 83 117 98 134 146 170 7 159 27 69 43 88 58 101 121 140 17 111 1178 75 166 87 37 54 126 150 12 22 114 103 72 160 82 93 50 171 33 137 14911 107 127 21 77 96 66 162 36 48 145 10 108 119 25 131 85 67 163 173 49141 39 106 152 5 122 90 20 74 164 56 132 32 110 143 100 8 120 154 80 6853 130 31 165

In the case of Table 48, Equation 21 may be expressed asY₀=X_(π(0))=X₉₂, Y₁=X_(π(1))=X₇₉, Y₂=X_(π(2))=X₁₆₈, . . . ,Y₁₇₈=X_(π(178))=X₃₁, and Y₁₇₉=X_(π(179))=X₁₆₅. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 92^(nd) bit group to the 0^(th) bitgroup, the 79^(th) bit group to the 1^(st) bit group, the 168^(th) bitgroup to the 2^(nd) bit group, . . . , the 31^(st) bit group to the178^(th) bit group, and the 165^(th) bit group to the 179^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 49 presented below.

TABLE 49 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 6 176 177 178179 π(j)-th block of 53 65 29 159 39 13 134 148 108 120 85 174 75 54 1641 21 44 95 130 144 118 154 Group-wise 33 76 58 106 167 11 96 0 23 136151 177 78 60 42 122 165 102 92 12 24 147 179 interleaver 82 67 52 38117 105 135 94 160 27 171 2 146 17 69 49 123 37 110 133 158 87 173 input98 8 19 57 72 121 36 132 149 86 176 100 7 26 59 73 166 47 112 153 84 14199 4 31 131 64 16 172 119 109 48 83 143 3 157 93 30 129 169 61 103 15113 71 142 43 456 89 32 5 168 124 56 104 77 138 18 152 114 178 46 163 2862 125 81 6 91 139 107 150 41 162 25 66 175 79 14 55 126 115 140 35 4590 68 101 161 9 80 22 128 111 145 50 34 70 97 170 155 10 20 127 116 13751 40 74 63 88

In the case of Table 49, Equation 21 may be expressed asY₀=X_(π(0))=X₅₃, Y₁=X_(π(1))=X₆₅, Y₂=X_(π(2))=X₂₉, . . . ,Y₁₇₈=X_(π(178))=X₆₃, and Y₁₇₉=X_(π(179))=X₈₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 53^(rd) bit group to the 0^(th) bitgroup, the 65^(th) bit group to the 1^(st) bit group, the 29^(th) bitgroup to the 2^(nd) bit group, . . . , the 63^(rd) bit group to the178^(th) bit group, and the 88^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 50 presented below.

TABLE 50 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56167 43 32 128 156 112 4 89 Group-wise 140 69 14 100 49 34 168 151 120 089 110 136 64 13 74 45 170 160 125 149 91 111 interleaver 2 139 55 67 4121 161 77 31 121 173 104 5 143 58 94 44 159 84 71 116 16 27 input 6 13357 106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 7696 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 123 36 15280 66 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10 126 48165 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98 109 2275 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29 102 9268 141 81 46

In the case of Table 50, Equation 21 may be expressed asY₀=X_(π(0))=X₁₈, Y₁=X_(π(1))=X₁₆₉, Y₂=X_(π(2))=X₃₀, . . . ,Y₁₇₈=X_(π(178))=X₈₁, and Y₁₇₉=X_(π(179))=X₄₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 18^(th) bit group to the 0^(th) bitgroup, the 169^(th) bit group to the 1^(st) bit group, the 30^(th) bitgroup to the 2^(nd) bit group, . . . , the 81^(st) bit group to the178^(th) bit group, and the 46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 51 presented below.

TABLE 51 Order of bits group to be block interleaved π(j) (0 < j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56167 43 32 128 156 112 4 89 Group-wise 140 69 14 100 49 34 168 151 120 086 110 136 64 13 74 45 170 160 125 149 91 111 interleaver 2 139 55 67 4121 161 77 31 121 173 104 5 143 58 94 44 159 84 71 116 16 27 input 6 13357 106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 7695 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 123 36 15280 66 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10 126 48163 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98 109 2275 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29 102 9268 141 81 46

In the case of Table 51, Equation 21 may be expressed asY₀=X_(π(0))=X₁₈, Y₁=X_(π(1))=X₁₆₉, Y₂=X_(π(2))=X₃₀, . . . ,Y₁₇₈=X_(π(178))=X₈₁, and Y₁₇₉=X_(π(179))=X₄₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 18^(th) bit group to the 0^(th) bitgroup, the 169^(th) bit group to the 1^(st) bit group, the 30^(th) bitgroup to the 2^(nd) bit group, . . . , the 81^(st) bit group to the178^(th) bit group, and the 46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 52 presented below.

TABLE 52 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 771 172 173 174 175 176 177 178179 π(j)-th block of 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56167 43 32 128 156 112 4 89 Group-wise 140 69 14 100 49 34 168 151 120 086 110 136 64 13 74 45 170 160 125 149 91 111 interleaver 2 139 55 67 4121 161 77 31 121 173 104 5 143 58 94 44 159 84 71 116 16 27 input 6 13357 106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 7696 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 123 36 15280 56 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10 126 48165 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98 109 2275 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29 102 9268 141 81 46

In the case of Table 52, Equation 21 may be expressed asY₀=X_(π(0))=X₁₈, Y₁=X_(π(0))=X₁₆₉, Y₂=X_(π(2))=X₃₀, . . . ,Y₁₇₈=X_(π(178))=X₈₁, and Y₁₇₉=X_(π(179))=X₄₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 18^(th) bit group to the 0^(th) bitgroup, the 169^(th) bit group to the 1^(st) bit group, the 30^(th) bitgroup to the 2^(nd) bit group, . . . , the 81^(st) bit group to the178^(th) bit group, and the 46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 53 presented below.

TABLE 53 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 43 150 26 119 108 7 173 163 81 135 71 45 153 55 92125 16 115 32 177 105 67 140 Group-wise 79 54 4 126 154 20 166 37 112 9564 144 76 48 5 134 124 25 160 176 88 59 100 interleaver 74 47 1 12 127137 36 178 90 162 22 147 117 72 101 2 132 33 52 84 157 172 21 input 14373 113 98 131 40 60 83 3 167 18 50 149 109 28 93 130 120 65 0 161 175 4415 77 148 104 91 114 66 133 165 29 46 56 17 152 105 86 122 6 75 170 13831 42 62 151 106 85 121 10 96 168 139 24 34 53 179 158 107 69 8 123 8797 141 38 169 23 57 156 111 13 70 80 99 128 35 145 171 49 155 110 11 6182 94 129 39 27 142 174 159 116 51 14 63 78 89 103 30 41 136 164 146 11819 68 9 58

In the case of Table 53, Equation 21 may be expressed asY₀=X_(π(0))=X₄₃, Y₁=X_(π(1))=X₁₅₀, Y₂=X_(π(2))=X₂₆, . . . ,Y₁₇₈=X_(π(178))=X₉, and Y₁₇₉=X_(π(179))=X₅₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 43^(rd) bit group to the 0^(th) bitgroup, the 150^(th) bit group to the 1^(st) bit group, the 26^(th) bitgroup to the 2^(nd) bit group, . . . , the 9^(th) bit group to the178^(th) bit group, and the 58^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 54 presented below.

TABLE 54 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 108 178 95 30 159 120 11 45 71 57 137 82 149 174 9633 117 127 160 19 67 52 0 Group-wise 81 179 141 102 37 115 128 163 63 12151 85 177 27 97 42 73 138 166 62 107 125 156 interleaver 15 25 89 17640 51 145 77 114 61 99 162 28 129 7 17 39 152 86 74 140 53 175 input 101123 2 13 31 165 88 155 143 41 59 110 132 70 9 24 171 91 122 146 48 36106 161 136 14 75 60 94 173 3 119 47 148 109 29 133 84 16 66 167 6 12149 157 104 26 144 134 93 72 169 1 38 55 116 103 18 153 142 83 126 65 8172 50 32 100 21 111 154 78 139 124 68 168 90 56 35 4 22 150 113 135 4679 69 38 164 58 34 5 147 118 23 44 130 80 92 105 64 170 54 10 158 20 43131 76 87 112

In the case of Table 54, Equation 21 may be expressed asY₀=X_(π(0))=X₁₀₈, Y₁=X_(π(1))=X₁₇₈, Y₂=X_(π(2))=X₉₅, . . . ,Y₁₇₈=X_(π(178))=X₈₇, and Y₁₇₉=X_(π(179))=X₁₁₂. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 108^(th) bit group to the 0^(th) bitgroup, the 178^(th) bit group to the 1^(st) bit group, the 95^(th) bitgroup to the 2^(nd) bit group, . . . , the 87^(th) bit group to the178^(th) bit group, and the 112^(th) bit group to the 179^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 55 presented below.

TABLE 55 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 57 154 144 171 111 5 38 82 15 122 99 54 26 151 136110 67 41 4 87 164 178 16 Group-wise 77 150 123 140 97 53 112 42 63 16523 78 7 126 176 138 89 153 40 116 65 28 163 interleaver 52 106 2 131 83147 12 177 95 32 167 44 59 114 73 84 139 149 124 13 27 101 0 input 61113 174 91 74 50 157 134 20 35 1 64 102 169 118 75 46 158 128 141 36 318 100 86 56 172 71 160 119 145 43 29 11 96 107 133 173 85 68 159 143 4937 24 117 6 130 179 80 66 104 142 166 48 17 33 92 120 132 79 156 62 109175 51 14 39 90 121 137 25 72 161 103 148 58 10 47 93 127 115 22 34 70162 152 60 8 105 45 129 81 94 30 19 170 146 69 9 55 108 135 125 98 31 8821 168 155 76

In the case of Table 55, Equation 21 may be expressed asY₀=X_(π(0))=X₅₇, Y₁=X_(π(1))=X₁₅₄, Y₂=X_(π(2))=X₁₄₄, . . . ,Y₁₇₈=X_(π(178))=X₁₅₅, and Y₁₇₉=X_(π(179))=X₇₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 57^(th) bit group to the 0^(th) bitgroup, the 154^(th) bit group to the 1^(st) bit group, the 144^(th) bitgroup to the 2^(nd) bit group, . . . , the 155^(th) bit group to the178^(th) bit group, and the 76^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 56 presented below.

TABLE 56 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 127 38 14 83 58 72 107 150 0 179 117 138 161 22 4482 32 100 56 5 60 120 133 Group-wise 168 17 157 147 87 104 39 4 60 29121 131 15 172 156 73 142 43 95 106 59 119 85 interleaver 21 7 153 17770 37 130 141 54 103 167 155 24 88 154 75 35 10 128 143 52 178 64 input112 89 166 99 34 13 76 155 134 48 65 114 23 145 2 98 124 12 86 159 46176 62 108 148 25 1 136 74 96 36 158 118 169 47 11 146 57 112 79 67 9430 111 170 160 3 144 49 125 19 84 61 101 113 171 71 9 31 135 45 149 9120 55 110 163 81 123 6 33 174 137 66 18 94 50 109 77 152 126 162 40 8 28173 93 140 63 78 151 122 51 41 105 27 165 30 175 139 80 68 16 129 116 5342 26 164 102 92

In the case of Table 56, Equation 21 may be expressed asY₀=X_(π(0))=X₁₂₇, Y₁=X_(π(1))=X₃₈, Y₂=X_(π(2))=X₁₄, . . . ,Y₁₇₈=X_(π(178))=X₁₀₂, and Y₁₇₉=X_(π(179))=X₉₂. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 127^(th) bit group to the 0^(th) bitgroup, the 38^(th) bit group to the 1^(st) bit group, the 14^(th) bitgroup to the 2^(nd) bit group, . . . , the 102^(nd) bit group to the178^(th) bit group, and the 92^(nd) bit group to the 179^(th) bit group.

As described above, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bit group wise by using Equation 21 andTables 32 to 56.

“j-th block of Group-wise Interleaver output” in Tables 32 to 56indicates the j-th bit group output from the group interleaver 122 afterinterleaving, and “π(j)-th block of Group-wise Interleaver input”indicates the π(j)-th bit group input to the group interleaver 122.

In addition, since the order of the bit groups constituting the LDPCcodeword is rearranged by the group interleaver 122 in bit group wise,and then the bit groups are block-interleaved by the block interleaver124, which will be described below, “Order of bits groups to be blockinterleaved” is set forth in Tables 32 to 56 in relation to π(j).

The LDPC codeword which is group-interleaved in the above-describedmethod is illustrated in FIG. 7. Comparing the LDPC codeword of FIG. 7and the LDPC codeword of FIG. 6 before group interleaving, it can beseen that the order of the plurality of bit groups constituting whereinQ_(ldpc) is a cyclic shift parameter value regarding columns in a columngroup of an information word submatrix of the parity check matrix,N_(ldpc) is a length of the LDPC codeword, and K_(ldpc) is a length ofinformation word bits of the LDPC codeword.

the LDPC codeword is rearranged.

That is, as shown in FIGS. 6 and 7, the groups of the LDPC codeword arearranged in order of bit group X₀, bit group X₁, . . . , bit groupX_(Ngroup-1) before being group-interleaved, and are arranged in anorder of bit group Y₀, bit group Y₁, . . . , bit group Y_(Ngroup-1)after being group-interleaved. In this case, the order of arranging thebit groups by the group interleaving may be determined based on Tables32 to 56.

The group twist interleaver 123 interleaves bits in a same group. Thatis, the group twist interleaver 123 may rearrange the order of the bitsin the same bit group by changing the order of the bits in the same bitgroup.

In this case, the group twist interleaver 123 may rearrange the order ofthe bits in the same bit group by cyclic-shifting a predetermined numberof bits from among the bits in the same bit group.

For example, as shown in FIG. 8, the group twist interleaver 123 maycyclic-shift bits included in the bit group Y₁ to the right by 1 bit. Inthis case, the bits located in the 0^(th) position, the 1^(st) position,the 2^(nd) position, . . . , the 358^(th) position, and the 359^(th)position in the bit group Y₁ as shown in FIG. 8 are cyclic-shifted tothe right by 1 bit. As a result, the bit located in the 359^(th)position before being cyclic-shifted is located in the front of the bitgroup Y₁ and the bits located in the 0^(th) position, the 1^(st)position, the 2^(nd) position, . . . , the 358^(th) position beforebeing cyclic-shifted are shifted to the right serially by 1 bit andlocated.

In addition, the group twist interleaver 123 may rearrange the order ofbits in each bit group by cyclic-shifting a different number of bits ineach bit group.

For example, the group twist interleaver 123 may cyclic-shift the bitsincluded in the bit group Y₁ to the right by 1 bit, and may cyclic-shiftthe bits included in the bit group Y₂ to the right by 3 bits.

However, the above-described group twist interleaver 123 may be omittedaccording to circumstances.

In addition, the group twist interleaver 123 is placed after the groupinterleaver 122 in the above-described example. However, this is merelyan example. That is, the group twist interleaver 123 changes only theorder of bits in a certain bit group and does not change the order ofthe bit groups. Therefore, the group twist interleaver 123 may be placedbefore the group interleaver 122.

The block interleaver 124 interleaves the plurality of bit groups theorder of which has been rearranged. Specifically, the block interleaver124 may interleave the plurality of bit groups the order of which hasbeen rearranged by the group interleaver 122 in bit group wise (or bitgroup unit). The block interleaver 124 is formed of a plurality ofcolumns each including a plurality of rows and may interleave bydividing the plurality of rearranged bit groups based on a modulationorder determined according to a modulation method.

In this case, the block interleaver 124 may interleave the plurality ofbit groups the order of which has been rearranged by the groupinterleaver 122 in bit group wise. Specifically, the block interleaver124 may interleave by dividing the plurality of rearranged bit groupsaccording to a modulation order by using a first part and a second part.

Specifically, the block interleaver 124 interleaves by dividing each ofthe plurality of columns into a first part and a second part, writingthe plurality of bit groups in the plurality of columns of the firstpart serially in bit group wise, dividing the bits of the other bitgroups into groups (or sub bit groups) each including a predeterminednumber of bits based on the number of columns, and writing the sub bitgroups in the plurality of columns of the second part serially.

Herein, the number of bit groups which are interleaved in bit group wisemay be determined by at least one of the number of rows and columnsconstituting the block interleaver 124, the number of bit groups and thenumber of bits included in each bit group. In other words, the blockinterleaver 124 may determine the bit groups which are to be interleavedin bit group wise considering at least one of the number of rows andcolumns constituting the block interleaver 124, the number of bit groupsand the number of bits included in each bit group, interleave thecorresponding bit groups in bit group wise, and divide bits of the otherbit groups into sub bit groups and interleave the sub bit groups. Forexample, the block interleaver 124 may interleave at least part of theplurality of bit groups in bit group wise using the first part, anddivide bits of the other bit groups into sub bit groups and interleavethe sub bit groups using the second part.

Meanwhile, interleaving bit groups in bit group wise means that the bitsincluded in the same bit group are written in the same column. In otherwords, the block interleaver 124, in case of bit groups which areinterleaved in bit group wise, may not divide the bits included in thesame bit groups and write the bits in the same column, and in case ofbit groups which are not interleaved in bit group wise, may divide thebits in the bit groups and write the bits in different columns.

Accordingly, the number of rows constituting the first part is amultiple of the number of bits included in one bit group (for example,360), and the number of rows constituting the second part may be lessthan the number of bits included in one bit group.

In addition, in all bit groups interleaved by the first part, the bitsincluded in the same bit group are written and interleaved in the samecolumn of the first part, and in at least one group interleaved by thesecond part, the bits are divided and written in at least two columns ofthe second part.

The specific interleaving method will be described later.

Meanwhile, the group twist interleaver 123 changes only the order ofbits in the bit group and does not change the order of bit groups byinterleaving. Accordingly, the order of the bit groups to beblock-interleaved by the block interleaver 124, that is, the order ofthe bit groups to be input to the block interleaver 124, may bedetermined by the group interleaver 122. Specifically, the order of thebit groups to be block-interleaved by the block interleaver 124 may bedetermined by π(j) defined in Tables 32 to 56.

As described above, the block interleaver 124 may interleave theplurality of bit groups the order of which has been rearranged in bitgroup wise by using the plurality of columns each including theplurality of rows.

In this case, the block interleaver 124 may interleave the LDPC codewordby dividing the plurality of columns into at least two parts. Forexample, the block interleaver 124 may divide each of the plurality ofcolumns into the first part and the second part and interleave theplurality of bit groups constituting the LDPC codeword.

In this case, the block interleaver 124 may divide each of the pluralityof columns into N number of parts (N is an integer greater than or equalto 2) according to whether the number of bit groups constituting theLDPC codeword is an integer multiple of the number of columnsconstituting the block interleaver 124, and may perform interleaving.

When the number of bit groups constituting the LDPC codeword is aninteger multiple of the number of columns constituting the blockinterleaver 124, the block interleaver 124 may interleave the pluralityof bit groups constituting the LDPC codeword in bit group wise withoutdividing each of the plurality of columns into parts.

Specifically, the block interleaver 124 may interleave by writing theplurality of bit groups of the LDPC codeword on each of the columns inbit group wise in a column direction, and reading each row of theplurality of columns in which the plurality of bit groups are written inbit group wise in a row direction.

In this case, the block interleaver 124 may interleave by writing bitsincluded in a predetermined number of bit groups which corresponds to aquotient obtained by dividing the number of bit groups of the LDPCcodeword by the number of columns of the block interleaver 124 on eachof the plurality of columns serially in a column direction, and readingeach row of the plurality of columns in which the bits are written in arow direction.

Hereinafter, the group located in the j^(th) position after beinginterleaved by the group interleaver 122 will be referred to as groupY₃.

For example, it is assumed that the block interleaver 124 is formed of Cnumber of columns each including R₁ number of rows. In addition, it isassumed that the LDPC codeword is formed of N_(group) number of bitgroups and the number of bit groups N_(group) is a multiple of C.

In this case, when the quotient obtained by dividing N_(group) number ofbit groups constituting the LDPC codeword by C number of columnsconstituting the block interleaver 124 is A (=N_(group)/C) (A is aninteger greater than 0), the block interleaver 124 may interleave bywriting A (=N_(group)/C) number of bit groups on each column serially ina column direction and reading bits written on each column in a rowdirection.

For example, as shown in FIG. 9, the block interleaver 124 writes bitsincluded in bit group Y₀, bit group Y₁, . . . , bit group Y_(A−1) in the1^(st) column from the 1^(st) row to the R₁ ^(th) row, writes bitsincluded in bit group Y_(A), bit group Y_(A+1), . . . , bit groupY_(2A−1) in the 2nd column from the 1^(st) row to the R₁ ^(th) row, . .. , and writes bits included in bit group Y_(CA−A) bit group Y_(CA−A+1),. . . , bit group Y_(CA−1) in the column C from the 1^(st) row to the R₁^(th) row. The block interleaver 124 may read the bits written in eachrow of the plurality of columns in a row direction.

Accordingly, the block interleaver 124 interleaves all bit groupsconstituting the LDPC codeword in bit group wise.

However, when the number of bit groups of the LDPC codeword is not aninteger multiple of the number of columns of the block interleaver 124,the block interleaver 124 may divide each column into 2 parts andinterleave a part of the plurality of bit groups of the LDPC codeword inbit group wise, and divide bits of the other bit groups into sub bitgroups and interleave the sub bit groups. In this case, the bitsincluded in the other bit groups, that is, the bits included in thenumber of groups which correspond to the remainder when the number ofbit groups constituting the LDPC codeword is divided by the number ofcolumns are not interleaved in bit group wise, but interleaved by beingdivided according to the number of columns.

Specifically, the block interleaver 124 may interleave the LDPC codewordby dividing each of the plurality of columns into two parts.

In this case, the block interleaver 124 may divide the plurality ofcolumns into the first part and the second part based on at least one ofthe number of columns of the block interleaver 124, the number of bitgroups of the LDPC codeword, and the number of bits of bit groups.

Here, each of the plurality of bit groups may be formed of 360 bits. Inaddition, the number of bit groups of the LDPC codeword is determinedbased on the length of the LDPC codeword and the number of bits includedin the bit group. For example, when an LDPC codeword in the length of16200 is divided such that each bit group has 360 bits, the LDPCcodeword is divided into 45 bit groups. Alternatively, when an LDPCcodeword in the length of 64800 is divided such that each bit group has360 bits, the LDPC codeword may be divided into 180 bit groups. Further,the number of columns constituting the block interleaver 124 may bedetermined according to a modulation method. This will be explained indetail below.

Accordingly, the number of rows constituting each of the first part andthe second part may be determined based on the number of columnsconstituting the block interleaver 124, the number of bit groupsconstituting the LDPC codeword, and the number of bits constituting eachof the plurality of bit groups.

Specifically, in each of the plurality of columns, the first part may beformed of as many rows as the number of bits included in at least onebit group which can be written in each column in bit group wise fromamong the plurality of bit groups of the LDPC codeword, according to thenumber of columns constituting the block interleaver 124, the number ofbit groups constituting the LDPC codeword, and the number of bitsconstituting each bit group.

In each of the plurality of columns, the second part may be formed ofrows excluding as many rows as the number of bits included in at leastsome bit groups which can be written in each of the plurality of columnsin bit group wise. Specifically, the number rows of the second part maybe the same value as a quotient when the number of bits included in allbit groups excluding bit groups corresponding to the first part isdivided by the number of columns constituting the block interleaver 124.In other words, the number of rows of the second part may be the samevalue as a quotient when the number of bits included in the remainingbit groups which are not written in the first part from among bit groupsconstituting the LDPC codeword is divided by the number of columns.

That is, the block interleaver 124 may divide each of the plurality ofcolumns into the first part including as many rows as the number of bitsincluded in bit groups which can be written in each column in bit groupwise, and the second part including the other rows.

Accordingly, the first part may be formed of as many rows as the numberof bits included in bit groups, that is, as many rows as an integermultiple of M. However, since the number of codeword bits constitutingeach bit group may be an aliquot part of M as described above, the firstpart may be formed of as many rows as an integer multiple of the numberof bits constituting each bit group.

In this case, the block interleaver 124 may interleave by writing andreading the LDPC codeword in the first part and the second part in thesame method.

Specifically, the block interleaver 124 may interleave by writing theLDPC codeword in the plurality of columns constituting each of the firstpart and the second part in a column direction, and reading theplurality of columns constituting the first part and the second part inwhich the LDPC codeword is written in a row direction.

That is, the block interleaver 124 may interleave by writing the bitsincluded in at least some bit groups which can be written in each of theplurality of columns in bit group wise in each of the plurality ofcolumns of the first part serially, dividing the bits included in theother bit groups except the at least some bit groups and writing in eachof the plurality of columns of the second part in a column direction,and reading the bits written in each of the plurality of columnsconstituting each of the first part and the second part in a rowdirection.

In this case, the block interleaver 124 may interleave by dividing theother bit groups except the at least some bit groups from among theplurality of bit groups based on the number of columns constituting theblock interleaver 124.

Specifically, the block interleaver 124 may interleave by dividing thebits included in the other bit groups by the number of a plurality ofcolumns, writing each of the divided bits in each of a plurality ofcolumns constituting the second part in a column direction, and readingthe plurality of columns constituting the second part, where the dividedbits are written, in a row direction.

That is, the block interleaver 124 may divide the bits included in theother bit groups except the bit groups written in the first part fromamong the plurality of bit groups of the LDPC codeword, that is, thebits in the number of bit groups which correspond to the remainder whenthe number of bit groups constituting the LDPC codeword is divided bythe number of columns, by the number of columns, and may write thedivided bits in each column of the second part serially in a columndirection.

For example, it is assumed that the block interleaver 124 is formed of Cnumber of columns each including R₁ number of rows. In addition, it isassumed that the LDPC codeword is formed of N_(group) number of bitgroups, the number of bit groups N_(group) is not a multiple of C, andA×C+1=N_(group) (A is an interger greater than 0). In other words, it isassumed that when the number of bit groups constituting the LDPCcodeword is divided by the number of columns, the quotient is A and theremainder is 1.

In this case, as shown in FIGS. 10 and 11, the block interleaver 124 maydivide each column into a first part including R₁ number of rows and asecond part including R₂ number of rows. In this case, R₁ may correspondto the number of bits included in bit groups which can be written ineach column in bit group wise, and R₂ may be R₁ subtracted from thenumber of rows of each column.

That is, in the above-described example, the number of bit groups whichcan be written in each column in bit group wise is A, and the first partof each column may be formed of as many rows as the number of bitsincluded in A number of bit groups, that is, may be formed of as manyrows as A×M number.

In this case, the block interleaver 124 writes the bits included in thebit groups which can be written in each column in bit group wise, thatis, A number of bit groups, in the first part of each column in thecolumn direction.

That is, as shown in FIGS. 10 and 11, the block interleaver 124 writesthe bits included in each of bit group Y₀, bit group Y₁, . . . , groupY_(A−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 1^(st)column, writes bits included in each of bit group Y_(A), bit groupY_(A+1), . . . , bit group Y_(2A−1) in the 1^(st) to R₁ ^(th) rows ofthe first part of the 2^(nd) column, . . . , writes bits included ineach of bit group Y_(CA−A), bit group Y_(CA−A+1), . . . , bit groupY_(CA−1) in the 1^(st) to R₁ ^(th) rows of the first part of the columnC.

As described above, the block interleaver 124 writes the bits includedin the bit groups which can be written in each column in bit group wisein the first part of each column.

In other words, in the above exemplary embodiment, the bits included ineach of bit group (Y₀), bit group (Y₁), . . . , bit group (Y_(A−1)) maynot be divided and all of the bits may be written in the first column,the bits included in each of bit group (Y_(A)), bit group (Y_(A+1)), . .. , bit group (Y_(2A−1)) may not be divided and all of the bits may bewritten in the second column, . . . , and the bits included in each ofbit group (Y_(CA−A)), bit group (Y_(CA−A+1)), . . . , group (Y_(CA−1))may not be divided and all of the bits may be written in the C column.As such, all bit groups interleaved by the first part are written in thesame column of the first part.

Thereafter, the block interleaver 124 divides bits included in the othergroups except the bit groups written in the first part of each columnfrom among the plurality of bit groups, and writes the bits in thesecond part of each column in the column direction. In this case, theblock interleaver 124 divides the bits included in the other bit groupsexcept the bit groups written in the first part of each column by thenumber of columns, so that the same number of bits are written in thesecond part of each column, and writes the divided bits in the secondpart of each column in the column direction.

In the above-described example, since A×C+1=N_(group), when the bitgroups constituting the LDPC codeword are written in the first partserially, the last bit group Y_(Ngroup-1) of the LDPC codeword is notwritten in the first part and remains. Accordingly, the blockinterleaver 124 divides the bits included in the bit group Y_(Ngroup-1)into C number of sub bit groups as shown in FIG. 10, and writes thedivided bits (that is, the bits corresponding to the quotient when thebits included in the last group (Y_(Ngroup-1)) are divided by C) in thesecond part of each column serially.

The bits divided based on the number of columns may be referred to assub bit groups. In this case, each of the sub bit groups may be writtenin each column of the second part. That is, the bits included in the bitgroups may be divided and may form the sub bit groups.

That is, the block interleaver 124 writes the bits in the 1^(st) to R₂throws of the second part of the 1^(st) column, writes the bits in the1^(st) to R₂ ^(th) rows of the second part of the 2^(nd) column, . . . ,and writes the bits in the 1^(st) to R₂ ^(th) rows of the second part ofthe column C. In this case, the block interleaver 124 may write the bitsin the second part of each column in the column direction as shown inFIG. 10.

That is, in the second part, the bits constituting the bit group may notbe written in the same column and may be written in the plurality ofcolumns. In other words, in the above example, the last bit group(Y_(Ngroup-1)) is formed of M number of bits and thus, the bits includedin the last bit group (Y_(Ngroup-1)) may be divided by M/C and writtenin each column. That is, the bits included in the last bit group(Y_(Ngroup-1)) are divided by M/C, forming M/C number of sub bit groups,and each of the sub bit groups may be written in each column of thesecond part.

Accordingly, in at least one bit group which is interleaved by thesecond part, the bits included in the at least one bit group are dividedand written in at least two columns constituting the second part.

In the above-described example, the block interleaver 124 writes thebits in the second part in the column direction. However, this is merelyan example. That is, the block interleaver 124 may write the bits in theplurality of columns of the second parts in a row direction. In thiscase, the block interleaver 124 may write the bits in the first part inthe same method as described above.

Specifically, referring to FIG. 11, the block interleaver 124 writes thebits from the 1^(st) row of the second part in the 1^(st) column to the1^(st) row of the second part in the column C, writes the bits from the2^(nd) row of the second part in the 1^(st) column to the 2^(nd) row ofthe second part in the column C, . . . , etc., and writes the bits fromthe R₂ ^(th) row of the second part in the 1^(st) column to the R₂ ^(th)row of the second part in the column C.

On the other hand, the block interleaver 124 reads the bits written ineach row of each part serially in the row direction. That is, as shownin FIGS. 10 and 11, the block interleaver 124 reads the bits written ineach row of the first part of the plurality of columns serially in therow direction, and reads the bits written in each row of the second partof the plurality of columns serially in the row direction.

Accordingly, the block interleaver 124 may interleave a part of theplurality of bit groups constituting the LDPC codeword in bit groupwise, and divide and interleave some of the remaining bit groups. Thatis, the block interleaver 124 may interleave by writing the LDPCcodeword constituting a predetermined number of bit groups from amongthe plurality of bit groups in the plurality of columns of the firstpart in bit group wise, dividing the bits of the other bit groups andwriting the bits in each of the columns of the second part, and readingthe plurality of columns of the first and second parts in the rowdirection.

As described above, the block interleaver 124 may interleave theplurality of bit groups in the methods described above with reference toFIGS. 9 to 11.

In particular, in the case of FIG. 10, the bits included in the bitgroup which does not belong to the first part are written in the secondpart in the column direction and read in the row direction. In view ofthis, the order of the bits included in the bit group which does notbelong to the first part is rearranged. Since the bits included in thebit group which does not belong to the first part are interleaved asdescribed above, Bit Error Rate (BER)/Frame Error Rate (FER) performancecan be improved in comparison with a case in which such bits are notinterleaved.

However, the bit group which does not belong to the first part may notbe interleaved as shown in FIG. 11. That is, since the block interleaver124 writes and read the bits included in the group which does not belongto the first part in and from the second part in the row direction, theorder of the bits included in the group which does not belong to thefirst part is not changed and the bits are output to the modulator 130serially. In this case, the bits included in the group which does notbelong to the first part may be output serially and mapped onto amodulation symbol.

In FIGS. 10 and 11, the last single bit group of the plurality of bitgroups is written in the second part. However, this is merely anexample. The number of bit groups written in the second part may varyaccording to the total number of bit groups of the LDPC codeword, thenumber of columns and rows, the number of transmission antennas, etc.

The block interleaver 124 may have a configuration as shown in Tables 57and 58 presented below:

TABLE 58 N_(ldpc) = 16200 QPSK 16 QAM 64 QAM 256 QAM 1024 QAM 4096 QAM C2 4 6 8 10 12 R₁ 7920 3960 2520 1800 1440 1080 R₂ 180 90 180 225 180 270

Herein, C (or N_(C)) is the number of columns of the block interleaver124, R₁ is the number of rows constituting the first part in eachcolumn, and R₂ is the number of rows constituting the second part ineach column.

Referring to Tables 57 and 58, the number of columns has the same valueas a modulation order according to a modulation method, and each of aplurality of columns is formed of rows corresponding to the number ofbits constituting the LDPC codeword divided by the number of a pluralityof columns.

For example, when the length N_(ldpc) of the LDPC codeword is 64800 andthe modulation method is QPSK, the block interleaver 124 is formed of 2columns as the modulation order is 2 in the case of QPSK, and eachcolumn is formed of rows as many as R₁+R₂=32400(=64800/2).

Meanwhile, referring to Tables 57 and 58, when the number of bit groupsconstituting an LDPC codeword is an integer multiple of the number ofcolumns, the block interleaver 124 interleaves without dividing eachcolumn. Therefore, R₁ corresponds to the number of rows constitutingeach column, and R₂ is 0. In addition, when the number of bit groupsconstituting an LDPC codeword is not an integer multiple of the numberof columns, the block interleaver 124 interleaves the groups by dividingeach column into the first part formed of R₁ number of rows, and thesecond part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is equal to thenumber of bits constituting a modulation symbol, bits included in a samebit group are mapped onto a single bit of each modulation symbol asshown in Tables 57 and 58.

For example, when N_(ldpc)=64800 and the modulation method is QPSK, theblock interleaver 124 may be formed of two (2) columns each including32400 rows. In this case, a plurality of bit groups are written in thetwo (2) columns in bit group wise and bits written in the same row ineach column are output serially. In this case, since two (2) bitsconstitute a single modulation symbol in the modulation method of QPSK,bits included in the same bit group, that is, bits output from a singlecolumn, may be mapped onto a single bit of each modulation symbol. Forexample, bits included in a bit group written in the 1^(St) column maybe mapped onto the first bit of each modulation symbol.

Referring to Tables 57 and 58, the total number of rows of the blockinterleaver 124, that is, R₁+R₂, is N_(ldpc)/C.

In addition, the number of rows of the first part, R₁, is an integermultiple of the number of bits included in each group, M (e.g., M=360),and maybe expressed as └N_(group)/C┘×M, and the number of rows of thesecond part, R₂, may be N_(ldpc)/C−R₁. Herein, └N_(group)/C┘ is thelargest integer below N_(group)/C. Since R₁ is an integer multiple ofthe number of bits included in each group, M, bits may be written in R₁in bit groups wise.

In addition, when the number of bit groups of the LDPC codeword is not amultiple of the number of columns, it can be seen from Tables 57 and 58that the block interleaver 124 interleaves by dividing each column intotwo parts.

Specifically, the length of the LDPC codeword divided by the number ofcolumns is the total number of rows included in the each column. In thiscase, when the number of bit groups of the LDPC codeword is a multipleof the number of columns, each column is not divided into two parts.However, when the number of bit groups of the LDPC codeword is not amultiple of the number of columns, each column is divided into twoparts.

For example, it is assumed that the number of columns of the blockinterleaver 124 is identical to the number of bits constituting amodulation symbol, and an LDPC codeword is formed of 64800 bits as shownin Table 57. In this case, each bit group of the LDPC codeword is formedof 360 bits, and the LDPC codeword is formed of 64800/360 (=180) bitgroups.

When the modulation method is QPSK, the block interleaver 124 may beformed of two (2) columns and each column may have 64800/2 (=32400)rows.

In this case, since the number of bit groups of the LDPC codeworddivided by the number of columns is 180/2 (=90), bits can be written ineach column in bit group wise without dividing each column into twoparts. That is, bits included in 90 bit groups which is the quotientwhen the number of bit groups constituting the LDPC codeword is dividedby the number of columns, that is, 90×360 (=32400) bits can be writtenin each column.

However, when the modulation method is 256-QAM, the block interleaver124 may be formed of eight (8) columns and each column may have64800/8(=8100) rows.

In this case, since the number of bit groups of the LDPC codeworddivided by the number of columns is 180/8=22.5, the number of bit groupsconstituting the LDPC codeword is not an integer multiple of the numberof columns. Accordingly, the block interleaver 124 divides each of theeight (8) columns into two parts to perform interleaving in bit groupwise.

In this case, since the bits should be written in the first part of eachcolumn in bit group wise, the number of bit groups which can be writtenin the first part of each column in bit group wise is 22 which is thequotient when the number of bit groups constituting the LDPC codeword isdivided by the number of columns, and accordingly, the first part ofeach column has 22×360 (=7920) rows. Accordingly, 7920 bits included in22 bit groups may be written in the first part of each column.

The second part of each column has rows which are the rows of the firstpart subtracted from the total rows of each column. Accordingly, thesecond part of each column includes 8100-7920 (=180) rows.

In this case, the bits included in the other bit groups which have notbeen written in the first part are divided and written in the secondpart of each column.

Specifically, since 22×8 (=176) bit groups are written in the firstpart, the number of bit groups to be written in the second part is180-176 (=4) (for example, bit group Y₁₇₆, bit group Y₁₇₇, bit groupY₁₇₈, and bit group Y₁₇₉ from among bit group Y₀, bit group Y₁, bitgroup Y₂, . . . , bit group Y₁₇₈, and bit group Y₁₇₉ constituting theLDPC codeword).

Accordingly, the block interleaver 124 may write the four (4) bit groupswhich have not been written in the first part and remains from among thegroups constituting the LDPC codeword in the second part of each columnserially.

That is, the block interleaver 124 may write 180 bits of the 360 bitsincluded in the bit group Y₁₇₆ in the 1^(st) row to the 180^(th) row ofthe second part of the 1^(st) column in the column direction, and maywrite the other 180 bits in the 1^(st) row to the 180^(th) row of thesecond part of the 2^(nd) column in the column direction. In addition,the block interleaver 124 may write 180 bits of the 360 bits included inthe bit group Y₁₇₇ in the 1^(st) row to the 180^(th) row of the secondpart of the 3^(rd) column in the column direction, and may write theother 180 bits in the 1^(st) row to the 180^(th) row of the second partof the 4^(th) column in the column direction. In addition, the blockinterleaver 124 may write 180 bits of the 360 bits included in the bitgroup Y₁₇₈ in the 1^(st) row to the 180^(th) row of the second part ofthe 5^(th) column in the column direction, and may write the other 180bits in the 1^(st) row to the 180^(th) row of the second part of the6^(th) column in the column direction. In addition, the blockinterleaver 124 may write 180 bits of the 360 bits included in the bitgroup Y₁₇₉ in the 1^(st) row to the 180^(th) row of the second part ofthe 7^(th) column in the column direction, and may write the other 180bits in the 1^(st) row to the 180^(th) row of the second part of the8^(th) column in the column direction.

Accordingly, the bits included in the bit group which has not beenwritten in the first part and remains are not written in the same columnin the second part and may be divided and written in the plurality ofcolumns.

Hereinafter, the block interleaver of FIG. 5 according to an exemplaryembodiment will be explained in detail with reference to FIG. 12.

In a group-interleaved LDPC codeword (v₀, v₁, . . . , ν_(N) _(ldpc) ₋₁),is continuously arranged like V={Y₀, Y₁, . . . Y_(N) _(group) ₋₁}.

The LDPC codeword after group interleaving may be interleaved by theblock interleaver 124 as shown in FIG. 12. In this case, the blockinterleaver 124 divide a plurality of columns into the first part(Part 1) and the second part (Part 2) based on the number of columns ofthe block interleaver 124 and the number of bits of bit groups. In thiscase, in the first part, the bits constituting the bit groups may bewritten in the same column, and in the second part, the bitsconstituting the bit groups may be written in a plurality of columns(i.e. the bits constituting the bit groups may be written in at leasttwo columns).

Specifically, input bits v_(i) are written serially from the first partto the second part column wise, and then read out serially from thefirst part to the second part row wise. That is, the data bits ν_(i) arewritten serially into the block interleaver column-wise starting in thefirst aprt and continuing column-wise finishing in the second part, andthen read out serially row-wise from the first part and then row-wisefrom the second part. Accordingly, the bit included in the same bitgroup in the first part may be mapped onto a single bit of eachmodulation symbol.

In this case, the number of columns and the number of rows of the firstpart and the second part of the block interleaver 124 vary according toa modulation format and a length of the LDPC codeword as in Table 30presented below. That is, the first part and the second part blockinterleaving configurations for each modulation format and code lengthare specified in Table 59 presented below. Herein, the number of columnsof the block interleaver 124 may be equal to the number of bitsconstituting a modulation symbol. In addition, a sum of the number ofrows of the first part, N_(r1) and the number of rows of the secondpart, N_(r2), is equal to N_(ldpc)/N_(C) (herein, N_(C) is the number ofcolumns). In addition, since N_(r1)(=└N_(group)/N_(c)┘×360) is amultiple of 360, a multiple of bit groups may be written in the firstpart.

TABLE 59 Rows in Part 1 N_(r1) Rows in Part 2 N_(r2) N_(ldpc) = N_(ldpc)= N_(ldpc) = N_(ldpc) = Columns Modulation 64800 16200 64800 16200 N_(C)QPSK 32400 7920 0 180 2  16-QAM 16200 3960 0 90 4  64-QAM 10800 2520 0180 6  256-QAM 7920 1800 180 225 8 1024-QAM 6480 1440 0 180 10 4096-QAM5400 1080 0 270 12

Hereinafter, an operation of the block interleaver 124 will be explainedin detail.

Specifically, as shown in FIG. 12, the input bit v_(i)(0≤i<N_(C)×N_(r1)) is written in r_(i) row of c_(i) column of the firstpart of the block interleaver 124. Herein, c_(i) and r_(i) are

$c_{i} = \left\lfloor \frac{i}{N_{r\; 1}} \right\rfloor$

and r_(i)=(i mod N_(r1)), respectively.

In addition, the input bit v_(i) (N_(C)×N_(r1)≤i<N_(ldpc)) is written inan r_(i) row of c_(i) column of the second part of the block interleaver124. Herein, c_(i) and r_(i) satisfy

$c_{i} = {{\left\lfloor \frac{\left( {i - {N_{C} \times N_{r\; 1}}} \right)}{N_{r\; 2}} \right\rfloor \mspace{14mu} {and}\mspace{14mu} r_{i}} = {N_{r\; 1} + \left\{ \left( {i - {N_{C} \times N_{r\; 1}}} \right) \right.}}$

mod N_(r2), respectively.

An output bit q_(j)(0≤j<N_(ldpc)) is read from c_(j) column of r_(j)row. Herein, r_(j) and c_(j) satisfy

$r_{j} = \left\lfloor \frac{j}{N_{c}} \right\rfloor$

and c_(j)=(j mod N_(C)), respectively.

For example, when the length N_(ldpc) of an LDPC codeword is 64800 andthe modulation method is 256-QAM, the order of bits output from theblock interleaver 124 may be (q₀, q₁, q₂, . . . , q₆₃₃₅₇, q₆₃₃₅₈,q₆₃₃₅₉, q₆₃₃₆₀, q₆₃₃₆₁, . . . , q₆₄₇₉₉)=(v₀, v₇₉₂₀, v₁₅₈₄₀, . . . ,v₄₇₅₁₉, v₅₅₄₃₉, v₆₃₃₅₉, v₆₃₃₆₀, v₆₃₅₄₀, . . . , v₆₄₇₉₉) Herein, theindexes of the right side of the foregoing equation may be specificallyexpressed for the eight (8) columns as 0, 7920, 15840, 23760, 31680,39600, 47520, 55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441,. . . , 7919, 15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360,63540, 63720, 63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719,63899, 64079, 64259, 64439, 64619, 64799.

Hereinafter, the interleaving operation of the block interleaver 124will be explained in detail.

The block interleaver 124 may interleave by writing a plurality of bitgroups in each column in bit group wise in a column direction, andreading each row of the plurality of columns in which the plurality ofbit groups are written in bit group wise in a row direction.

In this case, the number of columns constituting the block interleaver124 may vary according to a modulation method, and the number of rowsmay be the length of the LDPC codeword/the number of columns. Forexample, when the modulation method is QPSK, the block interleaver 124may be formed of 2 columns. In this case, when the length N_(ldpc) ofthe LDPC codeword is 16200, the number of rows is 8100 (=16200/2), and,when the length N_(ldpc) of the LDPC codeword is 64800, the number ofrows is 32400 (=64800/2).

Hereinafter, the method for interleaving the plurality of bit groups inbit group wise by the block interleaver 124 will be explained in detail.

When the number of bit groups constituting the LDPC codeword is aninteger multiple of the number of columns, the block interleaver 124 mayinterleave by writing the bit groups as many as the number of bit groupsdivided by the number of columns in each column serially in bit groupwise.

For example, when the modulation method is QPSK and the length N_(ldpc)of the LDPC codeword is 64800, the block interleaver 124 may be formedof two (2) columns each including 32400 rows. In this case, since theLDPC codeword is divided into (64800/360=180) number of bit groups whenthe length N_(ldpc) of the LDPC codeword is 64800, the number of bitgroups (=180) of the LDPC codeword may be an integer multiple of thenumber of columns (=2) when the modulation method is QPSK.

In this case, as shown in FIG. 13, the block interleaver 124 writes thebits included in each of the bit group Y₀, bit group Y₁ . . . , bitgroup Y₈₉ in the 1^(st) row to 32400^(th) row of the first column, andwrites the bits included in each of the bit group Y₉₀, the bit groupY₉₁, . . . , the bit group Y₁₇₉ in the 1^(st) row to 32400^(th) row ofthe second column. In addition, the block interleaver 124 may read thebits written in each row of the two columns serially in the rowdirection.

However, when the number of bit groups constituting the LDPC codeword isnot an integer multiple of the number of columns, the block interleaver124 may interleave by dividing each column into N number of parts (N isan integer greater than or equal to 2).

Specifically, the block interleaver 124 may divide each column into apart including as many rows as the number of bits included in the bitgroup which can be written in each column in bit group wise, and a partincluding the other rows, and may interleave by using the divided parts.

In this case, the block interleaver 124 may write at least some bitgroups which can be written in each of the plurality of columns in bitgroup wise from among the plurality of bit groups in each of theplurality of columns serially, and then divides the bits included in theother bit groups into sub bit groups and writes the bits in the otherarea remaining in each of the plurality of columns after the at leastsome bit groups are written in bit group wise. That is, the blockinterleaver 124 may write the bits included in at least some bit groupswhich are writable in the first part of each column in bit group wise,and may divide the bits included in the other bit groups and writhe thebits in the second part of each column.

For example, when the modulation method is QPSK and the length N_(ldpc)of the LDPC codeword is 16200, the block interleaver 124 may be formedof two (2) columns each including 8100 rows. In this case, since theLDPC codeword is divided into (16200/360=45) number of bit groups whenthe length N_(ldpc) of the LDPC codeword is 16200, the number of bitgroups (=45) of the LDPC codeword is not an integer multiple of thenumber of columns (=2) when the modulation method is QPSK. That is, aremainder exists.

In this case, the block interleaver 124 may divide each column into thefirst part including 7920 rows and the second part including 180 rows asshown in FIGS. 14 and 15.

The block interleaver 124 writes the bits included in the bit groupswhich can be written in each column in bit group wise in the first partof each column in the column direction.

That is, as shown in FIGS. 14 and 15, the block interleaver 124 writesthe bits included in each of the bit group Y₀, bit group Y₁ . . . , bitgroup Y₂₁ in the 1^(st) row to 7920^(th) row of the first part of thefirst column, and writes the bits included in each of the bit group Y₂₂,the bit group Y₂₃, . . . , the bit group Y₄₃ in the 1^(st) row to7920^(th) row of the first part of the second column.

As described above, the block interleaver 124 writes the bits includedin the bit groups which can be written in each column in bit group wisein the first part of each column in bit group wise.

Thereafter, the block interleaver 124 divides the bits included in theother bit groups except for the bit groups written in the first part ofeach column from among the plurality of bit groups, and writes the bitsin the second part of each column in the column direction. In this case,the block interleaver 124 may divide the bits included in the other bitgroups except for the bit groups written in the first part of eachcolumn by the number of columns, such that the same number of bits arewritten in the second part of each column, and writes the divided bitsin each column of the second part in the column direction.

For example, when the bit group Y₄₄, which is the last bit group of theLDPC codeword, remains as shown in FIG. 14, the block interleaver 124divides the bits included in the bit group Y₄₄ by 2, and writes thedivided bits in the second part of each column serially.

That is, the block interleaver 124 may write the bits in the 1^(st) rowto 180^(th) row of the second part of the first column, and writes thebits in the 1^(st) row to 180^(th) row of the second part of the secondcolumn. In this case, the block interleaver 124 may write the bits inthe second part of each column in the column direction as shown in FIG.14. That is, the bits constituting the bit group are not written in thesame column in the second part and are written in the plurality ofcolumns.

In the above-described example, the block interleaver 124 writes thebits in the second part in the column direction. However, this is merelyan example. That is, the block interleaver 124 may write the bits in theplurality of columns of the second part in the row direction. However,the block interleaver 124 may write the bits in the first part in thesame method as described above.

Specifically, referring to FIG. 15, the block interleaver 124 may writethe bits in the 1^(st) row of the second part of the first column to the1^(st) row of the second part of the second column, writes the bits inthe 2^(nd) row of the second part of the first column to the 2^(nd) rowof the second part of the second column, . . . , writes the bits in the180^(th) row of the second part of the first column to the 180^(th) rowof the second part of the second column.

The block interleaver 124 reads the bits written in each row of eachpart serially in the row direction. That is, as shown in FIGS. 14 and15, the block interleaver 124 may read the bits written in each row ofthe first part of the plurality of columns serially in the rowdirection, and may read the bits written in each row of the second partof the plurality of columns serially in the row direction.

As described above, the block interleaver 124 may interleave theplurality of bit groups in the method described above with reference toFIGS. 13 to 15.

The modulator 130 maps the interleaved LDPC codeword onto a modulationsymbol. Specifically, the modulator 130 may demultiplex the interleavedLDPC codeword, modulate the demultiplexed LDPC codeword, and map theLDPC codeword onto a constellation.

In this case, the modulator 130 may generate a modulation symbol usingthe bits included in each of a plurality of bit groups.

In other words, as described above, the bits included in different bitgroups are written in each column of the block interleaver 124, and theblock interleaver 124 reads the bits written in each column in the rowdirection. In this case, the modulator 130 generates a modulation symbolby mapping the bits read in each column onto each bit of the modulationsymbol. Accordingly, each bit of the modulation symbol belongs to adifferent group.

For example, it is assumed that the modulation symbol consists of Cnumber of bits. In this case, the bits which are read from each row of Cnumber of columns of the block interleaver 124 may be mapped onto eachbit of the modulation symbol and thus, each bit of the modulation symbolconsisting of C number of bits belong to C number of different groups.

Hereinbelow, the above feature will be described in greater detail.

First, the modulator 130 demultiplexes the interleaved LDPC codeword. Toachieve this, the modulator 130 may include a demultiplexer (not shown)to demultiplex the interleaved LDPC codeword.

The demultiplexer (not shown) demultiplexes the interleaved LDPCcodeword. Specifically, the demultiplexer (not shown) performsserial-to-parallel conversion with respect to the interleaved LDPCcodeword, and demultiplexes the interleaved LDPC codeword into a cellhaving a predetermined number of bits (or a data cell).

For example, as shown in FIG. 16, the demultiplexer (not shown) receivesan LDPC codeword Q=(q₀, q₁, q₂, . . . ) output from the interleaver 120,outputs the received LDPC codeword bits to a plurality of substreamsserially, converts the input LDPC codeword bits into cells, and outputsthe cells.

In this case, bits having a same index in each of the plurality ofsubstreams may constitute a same cell. Accordingly, the cells may beconfigured like (y_(0,0), y_(1,0), . . . , y_(η MOD−1,0))=(q₀, q₁,q_(η MOD−1)), (y_(0,1), y_(1,1), . . . , y_(η MOD−1,1))=(q_(η MOD),q_(η MOD+1), . . . , q_(2×η MOD−1)), . . . .

Herein, the number of substreams, N_(substreams), may be equal to thenumber of bits constituting a modulation symbol, η_(MOD). Accordingly,the number of bits constituting each cell may be equal to the number ofbits constituting a modulation symbol (that is, a modulation order).

For example, when the modulation method is QPSK, the number of bitsconstituting the modulation symbol, η_(MOD), is 2, and thus, the numberof substreams, N_(substreams), is 2, and the cells may be configuredlike (y_(0,0), y_(1,0))=(q₀, q₁), (y_(0,1), y_(1,1))=(q₂,q₃), (y_(0,2),y_(1,2))=(q₄, q₅), . . . .

The modulator 130 may map the demultiplexed LDPC codeword ontomodulation symbols.

Specifically, the modulator 130 may modulate bits (that is, cells)output from the demultiplexer (not shown) in various modulation methods.For example, when the modulation method is QPSK, 16-QAM, 64-QAM,256-QAM, 1024-QAM, and 4096-QAM, the number of bits constituting amodulation symbol, η_(MOD) (that is, the modulation order), may be 2, 4,6, 8, 10 and 12, respectively.

In this case, since each cell output from the demultiplexer (not shown)is formed of as many bits as the number of bits constituting amodulation symbol, the modulator 130 may generate a modulation symbol bymapping each cell output from the demultiplexer (not shown) onto aconstellation point serially. Herein, a modulation symbol corresponds toa constellation point on a constellation.

However, the above-described demultiplexer (not shown) may be omittedaccording to circumstances. In this case, the modulator 130 may generatemodulation symbols by grouping a predetermined number of bits frominterleaved bits serially and mapping the predetermined number of bitsonto constellation points. In this case, the modulator 130 may generatemodulation symbols by mapping η_(MOD) number of bits onto theconstellation points serially according to a modulation method.

When an LDPC codeword is generated based on the parity check matrixdefined as in Tables 4 to 21 and Tables 23 to 31, a plurality of bitgroups of the LDPC codeword are interleaved by using interleavingparameters defined as in Tables 32 to 56 for the following reasons.

In general, when modulation is performed by using QPSK,encoding/decoding performance depends on how LDPC codeword bits aremapped onto two bits of a QPSK symbol.

In particular, when two parity bits are connected to a single check nodein a parity check matrix, good performance can be guaranteed by mappingthe two parity bits onto a single QPSK symbol. In addition, goodperformance can be guaranteed by mapping two parity bits connected to asingle check node in the parity check matrix onto a single QPSK symbol.In addition, when there are a plurality of parity bits each connected toa single check node in a parity check matrix, good performance can beguaranteed by selecting two check nodes and mapping two parity bitsconnected to the two check nodes onto a single QPSK symbol.

Accordingly, after the LDPC codeword bits generated based on the paritycheck matrix defined as in Tables 4 to 21 and Tables 23 to 31 aregroup-interleaved based on Equation 21 and Tables 32 to 56, when theinterleaved LDPC codeword bits are modulated by QPSK, two parity bitsconnected to a single check node may be mapped onto a same QPSK symbolor two parity bits connected to the selected two check nodes may bemapped onto a same QPSK symbol. Accordingly, encoding/decodingperformance can be improved and the transmitting apparatus is robust toa burst error.

Specifically, since the order of bit groups to be written/read in theplurality of columns of the block interleaver 124 is determinedaccording to the interleaving in bit group wise in the group interleaver122, bits to be mapped onto a modulation symbol may be determinedaccording to the interleaving in bit group wise in the group interleaver122.

Accordingly, the group interleaver 122 may interleave the LDPC codewordbits in bit group wise such that bits belonging to a predeterminednumber of continuous bit groups, that is, bits connected to apredetermined number of same check nodes, are mapped onto a same QPSKsymbol, by considering reliability of bits mapped onto a modulationsymbol and performance of the codeword bits of the LDPC codeword. Toachieve this, the group interleaver 122 may interleave the LDPC codewordbits in bit group wise based on Equation 21 and Tables 32 to 56.

Hereinafter, a method for designing the group interleaver 122 accordingto an exemplary embodiment will be explained. For the convenience ofexplanation, a method for defining π(j) with reference to Table 33 fromamong Tables 32 to 56 by way of an example will be explained.

In the case of the QPSK modulation method, the block interleaver 124 isformed of two columns, and two bits read and output from a same row oftwo columns configure a same QPSK symbol. Accordingly, bits ofcontinuous bit groups from among the plurality of bit groups of the LDPCcodeword should be written in a same row in each of the two columns ofthe block interleaver 124 to be mapped onto a same QPSK symbol.

That is, in order to map two parity bits connected to a single checknode in the parity check matrix onto a same QPSK modulation symbol, bitsbelonging to two continuous bit groups to which the two parity bitsbelong should be written in a same row in each of the two columns of theblock interleaver 124.

When bits included in two continuous bit groups from the 25^(th) bitgroup to the 44^(th) bit group from among 45 bit groups constituting anLDPC codeword (that is, the 0^(th) to 44^(th) bit groups) should bemapped onto a same QPSK symbol for the purpose of improvingencoding/decoding performance, and it is assumed that the 26^(th) bitgroup, 28^(th) bit group, . . . , 42^(nd) bit group, and 44^(th) bitgroups are written in the 4321^(st) row to the 7920^(th) row of thefirst part of the first column of the block interleaver 124 as shown in(a) of FIG. 17, the 25^(th) bit group, 27^(th) bit group, . . . ,41^(st) bit group, and 43^(rd) bit group should be written in the4321^(st) row to the 7920^(th) row of the first part of the secondcolumn.

In this case, encoding/decoding performance depends on which bit groupsare mapped onto a same modulation symbol (in the above-describedexample, two continuous bit groups from the 25^(th) bit group to the44^(th) bit group are mapped onto the same modulation symbol).Therefore, the other bit groups may be randomly written in the blockinterleaver 124.

That is, in the above-described example, the 0^(th) bit group to the24^(th) bit group may be randomly written in the other rows of the firstpart and the second part which remain after the 25^(th) bit group to the44^(th) bit group are written in the block interleaver 124. For example,as shown in (a) of FIG. 17, the 3^(rd) bit group, 22^(nd) bit group,7^(th) bit group, . . . , 2^(nd) bit group, 23^(rd) bit group, 11^(th)bit group, 0^(th) bit group, 13^(th) bit group, . . . , 12^(th) bitgroup, and 16^(th) bit group may be written in the other rows of thefirst part, and the 8^(th) bit group may be written in the second part.

However, when the LDPC codeword bits are written in each column of theblock interleaver 124 in bit group wise as shown in (a) of FIG. 17, thebits included in the 25^(th) bit group to the 44^(th) bit group aremapped onto continuous QPSK symbols, and thus, are vulnerable to a busterror.

Accordingly, in order not to map the bits included in the 25^(th) bitgroup to the 44^(th) bit group onto continuous QPSK symbols, the rows ofthe block interleaver 124 may be randomly interleaved (row-wise randominterleaving) as shown in (a) of FIG. 17 and the order of the bit groupsto be written in the block interleaver 124 may be changed as shown in(b) of FIG. 17.

As a result, when the group interleaver 122 interleaves a plurality ofbit groups of an LDPC codeword in the order shown in Table 33, theplurality of bit groups of the LDPC codeword may be written in the blockinterleaver 124 in the order shown in (b) of FIG. 17, and accordingly,parity bits included in two continuous bit groups may be mapped onto asame QPSK symbol.

That is, when the encoder 110 performs LDPC-encoding in a code rate of7/15 based on a parity check matrix including an information wordsubmatrix defined by the Table 6 and a parity submatrix having a dualdiagonal configuration, and the plurality of bit groups of the LDPCcodeword are interleaved by the group interleaver 122 based on π(j)defined by Table 33, the plurality of bit groups of the LDPC codewordmay be written in the block interleaver 124 as shown in (b) of FIG. 17,and thus, bits included in two continuous bit groups of 20 bit groupsmay be mapped onto a same modulation symbol.

In (a) and (b) of FIG. 17, bits included in two continuous bit groups ofthe 20 bit groups from the 25^(th) bit group to the 44^(th) bit groupare mapped onto a same modulation symbol. However, this is merely anexample. The number of continuous bit groups to be mapped onto a samemodulation symbol may vary according to a parity check matrix and a coderate. That is, when LDPC encoding is performed with a parity checkmatrix having a different configuration and at a different code rate,the number of continuous bit groups to be mapped onto a same modulationsymbol may be changed.

Hereinafter, a method for defining π(j) with reference to Table 36according to another exemplary embodiment will be explained.

In the case of the QPSK modulation method, the block interleaver 124 isformed of two columns, and two bits read and output from a same row oftwo columns configure a same QPSK symbol. Accordingly, bits ofcontinuous bit groups from among a plurality of bit groups of an LDPCcodeword should be written in a same row in each of two columns of theblock interleaver 124 to be mapped onto a same QPSK symbol.

That is, in order to map two parity bits connected to a single checknode in a parity check matrix onto a same QPSK modulation symbol, bitsbelonging to two continuous bit groups to which the two parity bitsbelong should be written in a same row in each of two columns of theblock interleaver 124.

When bits included in two continuous bit groups from the 39^(th) bitgroup to the 44^(th) bit group from among 45 bit groups constituting anLDPC codeword (that is, the 0^(th) to 44^(th) bit groups) should bemapped onto a same QPSK symbol for the purpose of improvingencoding/decoding performance, and it is assumed that the 40^(th) bitgroup, 42^(nd) bit group, and 44^(th) bit groups are written in the6841^(st) row to the 7920^(th) row of the first part of the first columnof the block interleaver 124 as shown in (a) of FIG. 18, the 39^(th) bitgroup, 41^(st) bit group, and 43^(rd) bit group should be written in the6841^(st) row to the 7920^(th) row of the first part of the secondcolumn.

In this case, encoding/decoding performance depends on which bit groupsare mapped onto a same modulation symbol (in the above-describedexample, two continuous bit groups from the 39^(th) bit group to the44^(th) bit group are mapped onto a same modulation symbol). Therefore,the other bit groups may be randomly written in the block interleaver124.

That is, in the above-described example, the 0^(th) bit group to the38^(th) bit group may be randomly written in the other rows of the firstpart and the second part which remain after the 39^(th) bit group to the44^(th) bit group are written in the block interleaver 124. For example,as shown in (a) of FIG. 18, the 13^(th) bit group, 10^(th) bit group,0^(th) bit group, . . . , 36^(th) bit group, 38^(th) bit group, 6^(th)bit group, 7^(th) bit group, 17^(th) bit group, . . . , 35^(th) bitgroup, and 37^(th) bit group may be written in the other rows of thefirst part, and the 1^(st) bit group may be written in the second part.

However, when LDPC codeword bits are written in each column of the blockinterleaver 124 in bit group wise as shown in (a) of FIG. 18, bitsincluded in the 39^(th) bit group to the 44^(th) bit group are mappedonto continuous QPSK symbols, and thus, are vulnerable to a bust error.

Accordingly, in order not to map bits included in the 39^(th) bit groupto the 44^(th) bit group onto continuous QPSK symbols, the rows of theblock interleaver 124 may be randomly interleaved (row-wise randominterleaving) as shown in (a) of FIG. 18 and the order of the bit groupsto be written in the block interleaver 124 may be changed as shown in(b) of FIG. 18.

As a result, when the group interleaver 122 interleaves a plurality ofbit groups of an LDPC codeword in the order shown in Table 36, theplurality of bit groups of the LDPC codeword may be written in the blockinterleaver 124 in the order shown in (b) of FIG. 18, and accordingly,parity bits included in two continuous bit groups may be mapped onto asame QPSK symbol.

That is, when the encoder 110 performs LDPC-encoding in a code rate of13/15 based on a parity check matrix including an information wordsubmatrix defined by Table 12 and a parity submatrix having a dualdiagonal configuration, and the plurality of bit groups of the LDPCcodeword are interleaved by the group interleaver 122 based on π(j)defined by Table 36, the plurality of bit groups of the LDPC codewordmay be written in the block interleaver 124 as shown in (b) of FIG. 18,and thus, bits included in two continuous bit groups of 6 bit groups maybe mapped onto a same modulation symbol.

In (a) and (b) of FIG. 18, bits included in two continuous bit groups ofthe 6 bit groups from the 39^(th) bit group to the 44^(th) bit group aremapped onto a same modulation symbol. However, this is merely anexample. The number of continuous bit groups to be mapped onto a samemodulation symbol may vary according to a parity check matrix and a coderate. That is, when LDPC encoding is performed with a parity checkmatrix having a different configuration and at a different code rate,the number of continuous bit groups to be mapped onto a same modulationsymbol may be changed.

In addition, since performance is greatly affected by which continuousbit groups are mapped onto a same modulation symbol, the other bitgroups except for the continuous bit groups mapped onto the samemodulation symbol may be randomly written in the plurality of columns asshown in (a) and (b) of FIG. 17 or (a) and (b) of FIG. 18.

Accordingly, as long as a same bit group is mapped onto a samemodulation symbol, interleaving may be regarded as being performed inthe same method as the group interleaver presented in the presentdisclosure.

TABLE 60 A A_perm B_perm C_perm D_perm E_perm j-th (j)-th (j)-th (j)-th(j)-th (j)-th (j)-th block of block of block of block of block of blockof block of Group- Group- Group- Group- Group- Group- Group- wise wisewise wise wise wise wise Inter- Inter- Inter- Inter- Inter- Inter-Inter- leaver leaver leaver leaver leaver leaver leaver output inputinput input input input input 0 3 4 0 2 17 23 1 22 22 2 1 16 22 2 7 2319 3 18 24 3 18 44 44 44 44 44 4 6 34 34 34 34 34 5 1 1 10 17 0 9 6 4 311 15 3 7 7 14 2 9 16 2 5 8 5 32 32 32 32 32 9 15 42 42 42 42 42 10 2 620 6 12 18 11 23 15 23 7 11 19 12 26 30 30 30 30 30 13 28 40 40 40 40 4014 30 18 16 10 21 3 15 32 5 15 11 22 1 16 34 28 28 28 28 28 17 36 38 3838 38 38 18 38 7 6 21 8 14 19 40 14 5 22 7 13 20 42 26 26 26 26 26 21 4436 36 36 36 36 22 11 9 13 18 5 8 23 0 0 14 24 23 10 24 13 16 12 19 4 625 10 43 43 43 43 43 26 21 33 33 33 33 33 27 17 17 1 0 1 16 28 9 11 4 206 15 29 19 12 3 5 24 17 30 24 31 31 31 31 31 31 20 41 41 41 41 41 32 1221 18 4 19 4 33 16 20 17 9 20 2 34 25 29 29 29 29 29 35 27 39 39 39 3939 36 29 10 8 8 10 0 37 31 24 7 23 9 21 38 33 27 27 27 27 27 39 35 37 3737 37 37 40 37 13 24 12 14 20 41 39 19 22 13 15 12 42 41 25 25 25 25 2543 43 35 35 35 35 35 44 8 8 21 14 13 11

For example, in Table 60, A and A_perm indicate π(j) after/beforerow-wise random interleaving is performed, and B_perm, C_perm, D_perm,and E_perm indicate π(j) when row-wise random interleaving is performedafter the other bit groups except for continuous bit groups are randomlywritten in the plurality of columns in different methods. Referring toTable 60, in B_perm, C_perm, D_perm, and E_perm, the same group as inA_perm is mapped onto a same modulation symbol. Accordingly, it can beseen that a same interleaving method as in A_perm is used for B_perm,C_perm, D_perm, and E_perm.

In the above-described example, an interleaving pattern in the case of aparity check matrix having the configuration of FIG. 2 has beendescribed. Hereinafter, a method for designing an interleaving patternwhen a parity check matrix has the configuration of FIG. 4 will beexplained with reference to Table 32.

When there are bit groups formed of parity bits connected to a singlecheck node from among a plurality of bit groups of the LDPC codeword,bits included in two bit groups selected from the corresponding bitgroups should be written in a same row of two columns of the blockinterleaver 124.

It is assumed that the 18^(th) bit group to the 44^(th) bit group fromamong the 45 bit groups (that is, 0^(th) to 44^(th) bit groups) of anLDPC codeword are bit groups formed of parity bits connected to a singlecheck node connected to a single parity bit, and two bits are selectedfrom the corresponding bit groups and 2880 (=8×360) QPSK symbols intotal should be generated.

In this case, as shown in (a) of FIG. 19, 8 bit groups randomly selectedfrom among the 18^(th) bit group to the 44^(th) bit group should bewritten in the 5041^(st) row to the 7920^(th) row of the first part ofthe first column, and the other 8 bit groups randomly selected should bewritten in the 5041^(st) row to the 7920^(th) row of the first part ofthe second column.

Since encoding/decoding performance depends on how many QPSK symbols areformed of parity bits connected to a single check node connected to asingle parity bit, the other bit groups may be randomly written in theblock interleaver 124.

Accordingly, the 29 bit groups which are not selected in theabove-described example may be randomly written in the other rows of thefirst part, and the second part which remain after the selected groupsare written in the block interleaver 124. For example, as shown in (a)of FIG. 19, the 0^(th) bit group, 17^(th) bit group, 38^(th) bit group,. . . , 37^(th) bit group, 5^(th) bit group, and 3^(rd) bit group may bewritten in the other rows of the first part, and the 8^(th) bit groupmay be written in the second part.

However, when LDPC codeword bits are written in each column of the blockinterleaver 124 in bit group wise as shown in (a) of FIG. 19, a busterror may be intensively generated only in the parity bit, and thus, mayundermine encoding/decoding performance of the LDPC code. Accordingly,the rows of the block interleaver 124 may be randomly interleaved asshown in (a) of FIG. 19, and the order of the bit groups to be writtenin the block interleaver 124 may be changed as shown in (b) of FIG. 19,so that a bust error does not affect only the parity bit if any.

As a result, when the group interleaver 122 interleaves a plurality ofbit groups of an LDPC codeword in the order of Table 32, the pluralityof bit groups of the LDPC codeword may be written in the blockinterleaver 124 in the order shown in (b) of FIG. 19, and accordingly, aQPSK symbol formed of only parity bits connected to a check nodeconnected to a single parity bit may be generated.

That is, when the encoder 110 performs LDPC encoding based on the paritycheck matrix defined in Table 26 at a code rate of 5/15, and the groupinterleaver 122 interleaves a plurality of bit groups of an LDPCcodeword based on π(j) defined by Table 32, the plurality of bit groupsof the LDPC codeword may be written in the block interleaver 124 asshown in (b) of FIG. 19, and thus, bits included in two continuous bitgroups of 16 bit groups may be mapped onto a same modulation symbol.

In (a) and (b) of FIG. 19, only the 16 bit groups are randomly selectedfrom the 18^(th) bit group to the 44^(th) bit group and a modulationsymbol formed of only bits included in selected bit groups is generated.However, this is merely an example. The number of bit groups,corresponding to parity bits connected to a check node connected to asingle parity bit, which are mapped onto a same modulation symbol, maybe changed according to a parity check matrix and a code rate.

The transmitting apparatus 100 may transmit a modulation symbol to areceiving apparatus 1300. For example, the modulator 130 may map themodulation symbol onto an Orthogonal Frequency Division Multiplexing(OFDM) frame using OFDM, and may transmit the modulation symbol mappedonto the OFDM frame to the receiving apparatus 1300 through an allocatedchannel.

FIG. 20 is a block diagram to illustrate a configuration of a receivingapparatus according to an exemplary embodiment. Referring to FIG. 20,the receiving apparatus 1500 includes a demodulator 1510, a multiplexer1520, a deinterleaver 1530 and a decoder 1540.

The demodulator 1510 receives and demodulates a signal transmitted fromthe transmitting apparatus 100. Specifically, the demodulator 1510generates a value corresponding to an LDPC codeword by demodulating thereceived signal, and outputs the value to the multiplexer 1520. In thiscase, the demodulator 1510 may use a demodulation method correspondingto a modulation method used in the transmitting apparatus 100. To do so,the transmitting apparatus 100 may transmit information regarding themodulation method to the receiving apparatus 1500, or the transmittingapparatus 100 may perform modulation using a pre-defined modulationmethod between the transmitting apparatus 100 and the receivingapparatus 1500.

The value corresponding to the LDPC codeword may be expressed as achannel value for the received signal. There are various methods fordetermining the channel value, and for example, a method for determininga Log Likelihood Ratio (LLR) value may be the method for determining thechannel value.

The LLR value is a log value for a ratio of the probability that a bittransmitted from the transmitting apparatus 100 is 0 and the probabilitythat the bit is 1. In addition, the LLR value may be a bit value whichis determined by a hard decision, or may be a representative value whichis determined according to a section to which the probability that thebit transmitted from the transmitting apparatus 100 is 0 or 1 belongs.

The multiplexer 1520 multiplexes the output value of the demodulator1510 and outputs the value to the deinterleaver 1530.

Specifically, the multiplexer 1520 is an element corresponding to ademultiplexer (not shown) provided in the transmitting apparatus 100,and performs an operation corresponding to the demultiplexer (notshown). That is, the multiplexer 1520 performs an inverse operation ofthe operation of the demultiplexer (not shown), and performs cell-to-bitconversion with respect to the output value of the demodulator 1510 andoutputs the LLR value in the unit of bit. However, when thedemultiplexer (not shown) is omitted from the transmitting apparatus100, the multiplexer 1520 may be omitted from the receiving apparatus1500.

The information regarding whether the demultiplexing operation isperformed or not may be provided by the transmitting apparatus 100, ormay be pre-defined between the transmitting apparatus 100 and thereceiving apparatus 1500.

The deinterleaver 1530 deinterleaves the output value of the multiplexer1520 and outputs the values to the decoder 1540.

Specifically, the deinterleaver 1530 is an element corresponding to theinterleaver 120 of the transmitting apparatus 100 and performs anoperation corresponding to the interleaver 120. That is, thedeinterleaver 1530 deinterleaves the LLR value by performing theinterleaving operation of the interleaver 120 inversely.

To do so, the deinterleaver 1530 may include a block deinterleaver 1531,a group twist deinterleaver 1532, a group deinterleaver 1533, and aparity deinterleaver 1534 as shown in FIG. 21.

The block deinterleaver 1531 deinterleaves the output of the multiplexer1520 and outputs a value to the group twist deinterleaver 1532.

Specifically, the block deinterleaver 1531 is an element correspondingto the block interleaver 124 provided in the transmitting apparatus 100and performs the interleaving operation of the block interleaver 124inversely.

That is, the block deinterleaver 1531 deinterleaves by writing the LLRvalue output from the multiplexer 1520 in each row in the row directionand reading each column of the plurality of rows in which the LLR valueis written in the column direction by using at least one row formed ofthe plurality of columns.

In this case, when the block interleaver 124 interleaves by dividing thecolumn into two parts, the block deinterleaver 1531 may deinterleave bydividing the row into two parts.

In addition, when the block interleaver 124 writes and reads in and fromthe group that does not belong to the first part in the row direction,the block deinterleaver 1531 may deinterleave by writing and readingvalues corresponding to the group that does not belong to the first partin the row direction.

Hereinafter, the block deinterleaver 1531 will be explained withreference to FIG. 22. However, this is merely an example and the blockdeinterleaver 1531 may be implemented in other methods.

An input LLR v_(i) (0≤i<N_(ldpc)) is written in a r_(i) row and a c_(i)column of the block deinterleaver 1531. Herein, c_(i)=(i mod N_(c)) and

${r_{i} = \left\lfloor \frac{i}{N_{c}} \right\rfloor},$

On the other hand, an output LLR q_(i)(0≤i<N_(c)×N_(r1)) is read from ac_(i) column and a r_(i) row of the first part of the blockdeinterleaver 1531. Herein,

${c_{i} = \left\lfloor \frac{i}{N_{r\; 1}} \right\rfloor},$

r_(i)=(i mod N_(r1)).

In addition, an output LLR q₁(N_(c)×N_(r1)≤i<N_(ldpc)) is read from ac_(i) column and a r_(i) row of the second part. Herein,

${c_{i} = \left\lfloor \frac{\left( {i - {N_{c} \times N_{r\; 1}}} \right)}{N_{r\; 2}} \right\rfloor},$

r_(i)=N_(r1)+{(i−N_(c)×N_(r1)) mode N_(r2)}.

The group twist deinterleaver 1532 deinterleaves the output value of theblock deinterleaver 1531 and outputs the value to the groupdeinterleaver 1533.

Specifically, the group twist deinterleaver 1532 is an elementcorresponding to the group twist interleaver 123 provided in thetransmitting apparatus 100, and may perform the interleaving operationof the group twist interleaver 123 inversely.

That is, the group twist deinterleaver 1532 may rearrange the LLR valuesof the same bit group by changing the order of the LLR values existingin the same bit group. When the group twist operation is not performedin the transmitting apparatus 100, the group twist deinterleaver 1532may be omitted.

The group deinterleaver 1533 (or the group-wise deinterleaver)deinterleaves an output value of the group twist deinterleaver 1532 andoutputs a value to the parity deinterleaver 1534.

Specifically, the group deinterleaver 1533 is an element correspondingto the group interleaver 122 provided in the transmitting apparatus 100and may perform the interleaving operation of the group interleaver 122inversely.

That is, the group deinterleaver 1533 may rearrange the order of theplurality of bit groups in bit group wise. In this case, the groupdeinterleaver 1533 may rearrange the order of the plurality of bitgroups in bit group wise by applying the interleaving method of Tables32 to 56 inversely according to a length of the LDPC codeword, amodulation method and a code rate.

The parity deinterleaver 1534 performs parity deinterleaving withrespect to an output value of the group deinterleaver 1533 and outputs avalue to the decoder 1540.

Specifically, the parity deinterleaver 1534 is an element correspondingto the parity interleaver 121 provided in the transmitting apparatus 100and may perform the interleaving operation of the parity interleaver 121inversely. That is, the parity deinterleaver 1534 may deinterleave theLLR values corresponding to the parity bits from among the LLR valuesoutput from the group deinterleaver 1533. In this case, the paritydeinterleaver 1534 may deinterleave the LLR value corresponding to theparity bits inversely to the parity interleaving method of Equation 8.

However, the parity deinterleaver 1534 may be omitted depending on thedecoding method and embodiment of the decoder 1540.

Although the deinterleaver 1530 of FIG. 20 includes three (3) or four(4) elements as shown in FIG. 21, operations of the elements may beperformed by a single element. For example, when bits each of whichbelongs to each of bit groups X_(a) and X_(b) constitute a singlemodulation symbol, the deinterleaver 1530 may deinterleave these bits tolocations corresponding to their bit groups based on the received singlemodulation symbol.

For example, when the code rate is 13/15 and the modulation method isQPSK, the group deinterleaver 1533 may perform deinterleaving based onTable 36.

In this case, bits each of which belongs to each of bit groups Y₃(=X₃₈)and Y₂₅(=X₃₇) may constitute a single modulation symbol. Since one bitin each of the bit groups Y₃(=X₃₈) and Y₂₅(=X₃₇) constitutes a singlemodulation symbol, the deinterleaver 1530 may map bits onto decodinginitial values corresponding to the bit groups Y₃(=X₃₈) and Y₂₅(=X₃₇)based on the received single modulation symbol.

The decoder 1540 may perform LDPC decoding by using the output value ofthe deinterleaver 1530. To achieve this, the decoder 1540 may include anLDPC decoder (not shown) to perform the LDPC decoding.

Specifically, the decoder 1540 is an element corresponding to theencoder 110 of the transmitting apparatus 100 and may correct an errorby performing the LDPC decoding by using the LLR value output from thedeinterleaver 1530.

For example, the decoder 1540 may perform the LDPC decoding in aniterative decoding method based on a sum-product algorithm. Thesum-product algorithm is one example of a message passing algorithm, andthe message passing algorithm refers to an algorithm which exchangesmessages (e.g., LLR value) through an edge on a bipartite graph,calculates an output message from messages input to variable nodes orcheck nodes, and updates.

The decoder 1540 may use a parity check matrix when performing the LDPCdecoding. In this case, the parity check matrix used in the decoding mayhave the same configuration as that of the parity check matrix used inthe encoding of the encoder 110, and this has been described above withreference to FIGS. 2 to 4.

In addition, information on the parity check matrix and information onthe code rate, etc. which are used in the LDPC decoding may bepre-stored in the receiving apparatus 1500 or may be provided by thetransmitting apparatus 100.

FIG. 23 is a flowchart to illustrate an interleaving method of atransmitting apparatus according to an exemplary embodiment.

First, an LDPC codeword is generated by LDPC encoding based on a paritycheck matrix (S1710).

Thereafter, the LDPC codeword is interleaved (S1720). In this case, theLDPC codeword may be interleaved such that bits included in continuousbit groups from among a plurality of bit groups of the LDPC codeword aremapped onto a same modulation symbol. In addition, when there are aplurality of check nodes connected only to a single parity bit in theparity check matrix of the LDPC codeword, the LDPC codeword may beinterleaved such that bits included in bit groups corresponding to theparity bit connected to the corresponding check nodes are selectivelymapped onto a same modulation symbol.

Then, the interleaved LDPC codeword is mapped onto a modulation symbol(S1730). That is, the bits included in the continuous bit groups fromamong the plurality of bit groups of the LDPC codeword may be mappedonto a same modulation symbol. In addition, when there are a pluralityof check nodes connected only to a single parity bit in the parity checkmatrix of the LDPC codeword, the bits included in bit groupscorresponding to the parity bit connected to the corresponding checknodes may be selectively mapped onto a same modulation symbol.

Each of the plurality of bit groups may be formed of M number of bits,and M may be a common divisor of N_(ldpc) and K_(ldpc) and may bedetermined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Herein, Q_(ldpc)is a cyclic shift parameter value regarding columns in a column group ofan information word submatrix of the parity check matrix, N_(ldpc) is alength of the LDPC codeword, and K_(ldpc) is a length of informationword bits of the LDPC codeword.

Operation S1720 may include parity-interleaving parity bits of the LDPCcodeword, dividing the parity-interleaved LDPC codeword by the pluralityof bit groups and rearranging an order of the plurality of bit groups inbit group wise, and interleaving the plurality of bit groups the orderof which is rearranged.

The order of the plurality of bit groups may be rearranged in bit groupwise based on the above-described Equation 21 presented above.

In Equation 21, π(j) is determined based on at least one of a length ofthe LDPC codeword and a code rate.

For example, when the LDPC codeword has a length of 16200, themodulation method is QPSK, and the code rate is 13/15, π(j) in Equation21 may be defined as in Table 36 presented above.

Operation S1720 may include dividing the LDPC codeword by the pluralityof bit groups and rearranging an order of the plurality of bit groups inbit group wise, and interleaving the plurality of bit groups the orderof which is rearranged.

The order of the plurality of bit groups may be rearranged in bit groupwise based on Equation 21 presented above.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword and a code rate.

For example, when the LDPC codeword has a length of 16200, themodulation method is QPSK, and the code rate is 5/15, π(j) in Equation21 may be defined as in Table 32 presented above.

However, this is merely an example. The order of the plurality of bitgroups may be rearranged in bit group wise by using one of Tables 32 to56 and Equation 21.

The interleaving the plurality of bit groups may include: writing theplurality of bit groups in each of a plurality of columns in bit groupwise in a column direction, and reading each row of the plurality ofcolumns in which the plurality of bit groups are written in bit groupwise in a row direction.

In addition, the interleaving the plurality of bit groups may include:serially write, in the plurality of columns, at least some bit groupwhich is writable in the plurality of columns in bit group wise fromamong the plurality of bit groups, and then dividing and writing theother bit groups in an area which remains after the at least some bitgroup is written in the plurality of columns in bit group wise.

A non-transitory computer readable medium, which stores a program forperforming the interleaving methods according to various exemplaryembodiments in sequence, may be provided.

The non-transitory computer readable medium refers to a medium thatstores data semi-permanently rather than storing data for a very shorttime, such as a register, a cache, and a memory, and is readable by anapparatus. Specifically, the above-described various applications orprograms may be stored in a non-transitory computer readable medium suchas a compact disc (CD), a digital versatile disk (DVD), a hard disk, aBlu-ray disk, a universal serial bus (USB), a memory card, and a readonly memory (ROM), and may be provided.

At least one of the components, elements or units represented by a blockas illustrated in FIGS. 1, 5, 16, 20 and 21 may be embodied as variousnumbers of hardware, software and/or firmware structures that executerespective functions described above, according to an exemplaryembodiment. For example, at least one of these components, elements orunits may use a direct circuit structure, such as a memory, processing,logic, a look-up table, etc. that may execute the respective functionsthrough controls of one or more microprocessors or other controlapparatuses. Also, at least one of these components, elements or unitsmay be specifically embodied by a module, a program, or a part of code,which contains one or more executable instructions for performingspecified logic functions. Also, at least one of these components,elements or units may further include a processor such as a centralprocessing unit (CPU) that performs the respective functions, amicroprocessor, or the like. Further, although a bus is not illustratedin the above block diagrams, communication between the components,elements or units may be performed through the bus. Functional aspectsof the above exemplary embodiments may be implemented in algorithms thatexecute on one or more processors. Furthermore, the components, elementsor units represented by a block or processing steps may employ anynumber of related art techniques for electronics configuration, signalprocessing and/or control, data processing and the like.

The foregoing exemplary embodiments and advantages are merely exemplaryand are not to be construed as limiting the present inventive concept.The exemplary embodiments can be readily applied to other types ofapparatuses. Also, the description of the exemplary embodiments isintended to be illustrative, and not to limit the scope of the inventiveconcept, and many alternatives, modifications, and variations will beapparent to those skilled in the art.

What is claimed is:
 1. A receiving apparatus comprising: a receiverconfigured to receive a signal from a transmitting apparatus; ademodulator configured to demodulate the signal to generate valuesaccording to a quadrature phase shift keying (QPSK) modulation; adeinterleaver configured to split the values into a plurality of groupsand deinterleave the plurality of groups to provide deinterleavedvalues; and a decoder configured to decode the deinterleaved valuesbased on a low density parity check (LDPC) code having a code rate being5/15 and a code length being 16200 bits, wherein the plurality of groupsare deinterleaved based on a following equation:Y _(π(j)) =X _(j) for (0≤j<N _(group)), where X₃ is a j^(th) group amongthe plurality of groups, Y_(j) is a j^(th) group among the deinterleavedplurality of groups, N_(group) is a total number of the plurality ofgroups, and π(j) denotes a deinterleaving order for the deinterleaving,and wherein the π(j) is defined as follows: Order of deinterleaving π(j)(0 ≤ j < 45) Code j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2021 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 5/15 π(j) 35 7 29 11 14 32 38 28 20 17 25 39 19 4 1 12 10 30 0 4443 2 21 5 13 34 37 23 15 36 18 42 16 33 31 27 22 3 6 40 24 41 9 26 8


2. The receiving apparatus of claim 1, wherein each of the plurality ofgroups comprises 360 values.
 3. The receiving apparatus of claim 1,wherein π(j) is determined based on at least one of the code length, amodulation method and the code rate.